thermohydraulic performance improvement in heat exchanger

Research ArticleThermohydraulic Performance Improvement in Heat ExchangerSquare Duct Inserted with 45deg Inclined Square Ring

Amnart Boonloi 1 and Withada Jedsadaratanachai 2

1Department of Mechanical Engineering Technology College of Industrial TechnologyKing Mongkutrsquos University of Technology North Bangkok Bangkok 10800 ampailand2Department of Mechanical Engineering Faculty of Engineering King Mongkutrsquos Institute of Technology LadkrabangBangkok 10520 ampailand

Correspondence should be addressed to Withada Jedsadaratanachai kjwithadkmitlacth

Received 4 October 2019 Revised 7 December 2019 Accepted 16 December 2019 Published 13 January 2020

Academic Editor Joseph Virgone

Copyright copy 2020 Amnart Boonloi and Withada Jedsadaratanachai -is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

-ermal performance development heat transfer structure and flow behavior in the heat exchanger square duct equippedwith a 45deg inclined square ring are investigated numerically -e effects of flow blockage ratios and spacing ratios for theinclined square ring on fluid flow and heat transfer are considered -e Reynolds number (Re 100ndash2000 laminar regime)based on the hydraulic diameter of the square duct is selected for the present work -e numerical domain of the square ductinserted with the 45deg inclined square ring is solved with the finite volume method -e SIMPLE algorithm is picked for thenumerical investigation -e heat transfer characteristics and flow topologies in the square duct inserted with the inclinedsquare ring are plotted in the numerical report -e heat transfer rate pressure loss and efficiency for the square duct placedwith the inclined square ring are presented in forms of Nusselt number friction factor and thermal enhancement factorrespectively As the numerical results it is detected that the heat transfer rate of the heat exchanger square duct inserted withthe inclined square ring is around 100ndash1005 times over the smooth duct with no inclined square ring Additionally themaximum thermal enhancement factor for the heat exchanger square duct inserted with the inclined square ring isaround 284

1 Introduction

-e effort to develop the thermal performance of the heattransfer system in various industries and engineering deviceshad been considered bymany researchers-e improvementof the heat transfer rate and thermal performance in the heatexchanger can be done by two methods -e first method iscalled ldquoactive methodrdquo -e active method requires addi-tional power such as vibration to improve heat transfer rate-e second method is named ldquopassive methodrdquo -e passivemethod is to produce the vortex flow to disturb the thermalboundary layer on the heat transfer surface -e passivemethod is done by installing the vortex generators or tur-bulators in the heating system Rib [1ndash8] baffle [9ndash13]winglet [14ndash19] etc are types of the vortex generators

-e types configuration parameter etc of the vortexgenerators had been studied and developed by manyresearchers For example Chamoli et al [20] numericallyinvestigated the thermal performance augmentation in acircular tube with novel anchor-shaped vortex generatorsfor the Reynolds number around 3000ndash18000 -eyconcluded that the heat transfer rate and friction loss forthe circular tube with the novel anchor-shaped vortexgenerators are higher than the plain tube around224ndash456 and 401ndash2323 times respectively -ey alsofound that the maximum thermal enhancement factor forthe circular tube with the novel anchor-shaped vortexgenerators is around 172 Bartwal et al [21] reported theheat transfer increment in the heat exchanger by thecircular ring with a wire net -ey summarized that the

HindawiModelling and Simulation in EngineeringVolume 2020 Article ID 3862624 22 pageshttpsdoiorg10115520203862624

heat transfer in the heat exchanger is greater than thesmooth tube around 335 times while the maximumthermal performance is around 284 Chamoli et al [22]presented the thermal performance of a solar air heaterplaced with the winglet vortex generator -e effects of tipedge ratio and flow attack angle for the winglet on heattransfer pressure loss and performance were studied forRe 3500ndash16000 -ey claimed the winglet vortex gen-erator in the heat exchanger gives the best thermalperformance in the range 172ndash220 Singh et al [23]studied the influences of the perforated hollow circularcylinder in a circular tube for Re 6000ndash27000 -eyfound that the perforated hollow circular cylinder in thecircular tube provides the heat transfer rate around150ndash230 when compared with the smooth tube Cha-moli et al [24] illustrated the convective heat transfer in acircular tube fitted with perforated vortex generators -eeffects of the perforation index and relative pitch lengthon heat transfer and thermal performance in the testedtube were considered for Re 3000ndash21000 -ey foundthat the circular tube with perforated vortex generatorsprovides the maximum thermal enhancement factoraround 165 -e multiobjective shape optimization of aheat exchanger tube fitted with compound inserts wasreported by Chamoli et al [25] Sawhney et al [26] ex-perimentally examined the heat transfer and frictionfactor in a solar air heater duct with wavy delta wingletsfor the Reynolds number around 4000ndash17300 -enumber of wave and relative longitudinal pitch for thewavy delta winglet was compared -ey claimed that thewavy delta winglet in the duct performs the heat transferrate greater than the plain duct around 223

-e objective for the present research is to design thevortex generator with the special conditions as follows

(i) -e new design has high effectiveness to increaseheat transfer rate in the heat exchanger section

(ii) -e installation and maintenance of the vortexgenerator in the heat exchanger are stable andconvenient

(iii) -e production of the vortex generator is notcomplicated

In the present research the passive method is focused-e inclined square ring (ISR) like the baffle or thin rib isselected to improve heat transfer rate and performance inthe heat exchanger square duct -e parameter of the ISRand placement in the heating duct is investigated nu-merically in three dimensions-e numerical investigationmay help to describe the flow and heat transfer structuresin the heating section -e understanding on flow and heattransfer behaviors in the heat exchanger is an importantfactor for the development of the compact heat exchanger-e numerical study also saves the cost and resource forthe studied process when compared with the experimentalexamination -e numerical results are plotted in terms offlow and heat transfer configurations in the tested sectionsuch as temperature contour Nux Contour and stream-lines-e performance analysis in form of Nusselt number

friction factor and thermal enhancement factor for theheat exchanger square duct equipped with ISR is alsoconcluded

2 Tested Section with 45deg ISR

-e computational domain of the heat exchanger squareduct inserted with the 45deg ISR is plotted in Figure 1 -ephysical domain of the square duct inserted with the 45degISR in y-z plane is depicted as Figure 2 -e height of thesquare ductH is around 005m-e duct height is equal tothe hydraulic diameter or HDh -e ISRs are inserted inthe square duct with single pitch spacing ratio of 1 (PH 1) in all investigated cases -e ratio between the ISRheight b and channel height H or bH is varied in therange 005ndash030 -e spacing between the outer edge of theISR and the channel wall s is varied in terms of spacingratio or sH 0ndash030 -e air flow rate is presented in theform of Reynolds number -e Reynolds number at theinlet condition around 100ndash2000 is considered for thecurrent work -e numerical models with the mesh of theheat exchanger square duct inserted with the 45deg ISR areillustrated as Figures 3(a) and 3(b) for sH 0 and 020respectively at bH 020

3 Numerical Method

-e flow is a laminar regime with the Reynolds numberbased on the hydraulic diameter -e flow and heat transferare steady in three dimensions -e tested fluid is set asincompressible flow -e tested fluid is air with the Prandtlnumber around 0707 (300K) -e thermal properties of theair are counted to be constant at the average bulk meantemperature -e heat transfer in the force convection modeis considered for the present work while the radiation andnatural convection are ignored -e body force and viscousdissipation are also disregarded No slip wall condition isapplied for all channel surfaces and ISR -e periodiccondition [27] on both flow and heat transfer is applied forthe inlet and outlet of the computational domain -e ISR isassumed to be an insulator while the duct walls are set withconstant temperature around 310K -e flow and heattransfer in the heat exchanger duct fitted with the ISR are infully developed condition [28]

-e finite volume with the SIMPLE algorithm is selectedto solve the present investigation -e present model isanswered by the continuity the NavierndashStokes equationsand the energy equation which are illustrated as equations(1)ndash(3) respectively -e continuity equation momentumequation and energy equation are discretized by the powerlaw scheme power law scheme and QUICK scheme re-spectively -e numerical solutions are considered to beconverged when the normalized residual values are less than10minus 5 for all variables but less than 10minus 9 only for the energyequation

Continuity equation

z

zxi

ρui( 1113857 0 (1)

2 Modelling and Simulation in Engineering

Inclined ring

Inclined ring

Periodic module(bH = 020 sH = 0)

Periodic module(bH = sH = 020)

bH = sH = 020

Inclined ring

Channel wall

Flow direction

Flow direction

s

b

P

P

yxz

H = D h

y

xz

yxz

Figure 1 Computational domain of the heat exchanger square duct installed with the 45deg ISR

bH = 010

bH = 015

bH = 020

bH = 025

bH = 030

0 005 010 015 020 025 030sH

bH = 005

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

Figure 2 Square duct installed with the 45deg ISR in the y-z plane at various cases

Modelling and Simulation in Engineering 3

Momentum equation

z ρuiuj1113872 1113873

zxj

minuszp

zxi

+z

zxj

μzui

zxj

+zuj

zxi

1113888 11138891113890 1113891 (2)

Energy equation

z

zxi

ρuiT( 1113857 z

zxj

ΓzT

zxj

1113888 1113889 (3)

where Γ is the thermal diffusivity and is printed as follows

Γ μPr

(4)

-e tested fluid is offered in terms of the Reynoldsnumber based on the hydraulic diameter of the square ductDh -e hydraulic diameter of the square duct is equal toduct height (Dh H) -e Reynolds number is written asfollows

Re ρuDh

μ (5)

-e pressure loss of the square duct equipped with the45deg ISR is reported in the form of friction factor ΔP is thepressure drop across the periodic module -e length of theperiodic module is presented with L -e friction factor canbe determined as follows

f (ΔPL)Dh

(12)ρu2 (6)

-e heat transfer rate in the heat exchanger square ductinserted with the 45deg ISR is presented with the local Nusseltnumber and average Nusselt number as follows

Nux hxDh

k (7)

Nu 1L

1113946Nuxzx (8)

-e thermal efficiency of the heat exchanger ductequipped with the 45deg ISR is presented in the form of thermalenhancement factor or TEF as equation (9) -e thermalenhancement factor is defined as the ratio of the heat transfer

coefficient of an augmented surface h to that of a smoothsurface h0 at similar pumping power

TEF h

h0

11138681113868111386811138681113868111386811138681113868ppNuNu0

11138681113868111386811138681113868111386811138681113868pp

NuNu0( 1113857

ff0( 111385713 (9)

Nu0 and f0 are the Nusselt number and friction factor forthe smooth square duct respectively

4 Numerical Validation

It is necessary to ensure that the computational domain ofthe square duct inserted with the 45deg ISR has enough reli-ability to predict flow and heat transfer mechanisms in thetested section-e numerical model of this work is validated-e model validation can be divided into two sectionsvalidation of the smooth duct and grid independence -everification of the smooth square duct is done by comparingbetween the present results with the values on both Nusseltnumber and friction factor from the correlations [29] -edeviations of both values are around plusmn2 and plusmn25 for theNusselt number and friction factor respectively -e veri-fication of the smooth square duct for heat transfer andpressure loss is plotted as Figure 4

-e comparison between five similar models (bH sH 020) with different grid cells 80000 120000 180000240000 and 360000 is done It is found that the compu-tational domain with the grid around 120000ndash360000 givessimilar results for both heat transfer rate and friction loss-erefore the grid around 120000 is applied for all in-vestigated cases of the heat exchanger square duct insertedwith the 45deg ISR As the preliminary result it can be con-cluded that the numerical model of the heat exchangersquare duct inserted with 45deg ISR has enough confidentialityto study flow and heat transfer characteristics -e gridindependence of the present investigation is reported asFigures 5(a) and 5(b) for Nusselt number ratio and frictionfactor ratio respectively

5 Numerical Result

-e numerical result of the heat exchanger square ductinserted with the 45deg ISR is separated into two sectionsmechanism in the tested duct and performance analysis -estreamlines in transverse planes temperature distributions

yxz

(a)

yxz

(b)

Figure 3 Computational domain with the mesh of the heat exchanger square duct installed with the 45degISR for (a) bH 020 sH 0 and(b) bH sH 020


in transverse planes and local Nusselt number distributionsin the studied section are plotted in the first part of thenumerical result -e heat transfer rate pressure loss andthermal efficiency of the heating duct installed with the 45degISR are concluded at the performance analysis part in termsof Nusselt number friction factor and thermal enhance-ment factor respectively

51 Mechanisms in the Square Duct Equipped with 45deg ISR-e streamlines in y-z planes of the heat exchanger squareduct installed with the 45deg ISR are illustrated as Figures 6(a)ndash6(g) respectively for sH 0 005 010 015 020 025 and030 at bH 020 and Re 800 -e installation of the 45degISR in the heating section can produce the vortex flow For sH 0 the two main vortex flows are found at the upper andlower parts of the plane When sHgt 0 the small vorticesnear the duct walls are detected -e vortices near the duct

wall are found to be larger when enhancing the sH value-e flow description in the heating duct is presented asFigure 7 -e vortex flow in the heating duct will disturb thethermal boundary layer on the duct wall -e thermalboundary layer disturbance in the heating duct is the reasonfor heat transfer coefficient and performance augmentations-e vortex flow in the tested section also helps for a better airtemperature mixing that is another cause for heat transferand thermal performance increments -e presence of thespacing between the outer edge of the ISR and the duct wallmay decrease the strength of the main vortex flow or in-crease the turbulent fluid mixing

-e thermal boundary layer disturbance in the testedsection equipped with the 45deg ISR can be considered fromthe temperature distributions in transverse planesFigures 8(a)ndash8(g) report the temperature contours intransverse planes of the heating section installed with the 45degISR for sH 0 005 010 015 020 025 and 030

Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Nu

Nu 0

0

1

2

3

4

5

6

7

8

bH = sH = 020

80000 cells120000 cells180000 cells

240000 cells360000 cells

(a)

ff0

02468

1012141618202224262830

bH = sH = 020

Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200



(b)

Figure 5 Grid independence for (a) Nusselt number ratio and (b) friction factor ratio

Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

f0

00

01

02

03

04

05

06

07

Nu 0

26

28

30

32

34

f0 correlationf0 present result

Nu0 correlationNu0 present result

Figure 4 Verification of the smooth square duct


yxz

(a)

yxz

(b)y

xz

(c)

yxz

(d)y

xz

(e)

yxz

(f)y

xz

(g)

Figure 6 Streamlines in the y-z plane of the heat exchanger square duct installed with the 45deg ISR for (a) sH 0 (b) sH 005 (c) sH 010 (d) sH 015 (e) sH 020 (f ) sH 025 and (g) sH 030 at BR 020 and Re 800


Main vortex core

Main vortexcore

Small vortices

Figure 7 Flow description

(a) (b)

(c) (d)

(e) (f )

Figure 8 Continued


respectively at Re 800 and bH 020 In general theblue contour (low-temperature air) is found at the centerof the square duct while the red contour (high-tem-perature fluid) is detected near the duct walls for thesmooth duct with no ISR -e vortex flow which iscreated by the 45deg ISR in the heating system can disturbthe thermal boundary layer in all cases As shown infigures the blue layer distributes from the center of theplane while the red layer is found to decrease whencompared with the smooth duct -e thickness of the redlayer near the duct walls extremely decreases when sH gt 010 -e configuration of the heat transfer is notsimilar when the sH value is changed -e sH valuearound 015ndash030 gives the better fluid mixing than the sH value around 0ndash010

-e local Nusselt number distributions on the duct wallsof the heat exchanger square duct inserted with the 45deg ISRare plotted as Figures 9ndash14 respectively at Re 800 of bH 005 010 015 020 025 and 030-e wall code for theheat exchanger square duct inserted with the 45deg ISR isprinted as Figure 15 For bH 005 sH 005 provides thehighest heat transfer rate at wallA and wallB -e localNusselt number at wallA and wallB decreases when in-creasing sH value but the local Nusselt number at wallC andwallD performs the reverse trend

Seeing at bH 010 the local Nusselt number at wallCand wallD enhances when augmenting sH sH 0 shows thehighest heat transfer rate at wallA and wallB -e lowest heattransfer rate at wallA and wallB is found at sH 005

Considering at bH 015 Nux at wallC and wallD en-hances when increasing sH At wallA and wallB sH 030gives the highest heat transfer rate while sH 0 performsthe opposite result -e peak of the local Nusselt number atwallA and wallB is found at sH 015ndash025

For bH 020 at wallA and wallB the maximum value ofthe local Nusselt number is found at sH 015ndash020 -epeak of heat transfer rate at wallC and wallD is detected at sH 020ndash030

At bH 025 the highest heat transfer rate at wallA andwallB is found at sH 010ndash015 For all duct walls the localNusselt number enhances when 0le sHle 015 but decreaseswhen sHgt 015

For bH 030 the maximum value of heat transfer rateat wallA and wallB appears at sH 010 Considering allsidewalls of the duct the local Nusselt number developswhen 0le sHle 015 but drops when sHgt 015

Considering a similar sH value the augmentation on bH of the 45deg ISR brings very close structure in both heattransfer and flow behaviors in the heat exchanger duct

52 Performance Analysis -e Nusselt number ratio isplotted with the Reynolds number at various sH values forbH 005 010 015 020 025 and 030 as Figures 16(a)ndash16(f ) respectively -e heat exchanger square duct insertedwith the 45deg ISR brings higher heat transfer rate than thesmooth duct in all investigated cases NuNu0 is greater thanthe unity In most cases the Nusselt number enhances whenaugmenting the Reynolds number In the range investigatedthe average Nusselt number is around 102ndash246 102ndash444103ndash568 115ndash727 136ndash1005 and 154ndash930 times overthe smooth square duct for bH 005 010 015 020 025and 030 respectively

-e relation of the friction factor ratio with the Reynoldsnumber for the heating duct installed with the 45deg ISR isplotted as Figures 17(a)ndash17(f ) respectively for bH 005010 015 020 025 and 030 -e attachment of the 45deg ISRin the heat exchanger square channel provides higherfriction loss than the smooth duct with no ISR -e frictionfactor increases when increasing the Reynolds number -eextreme increment of the friction loss is found at high bHand Re values sH 0 provides the lowest friction loss in allbH values

Seeing at bH 005 and 0le sHle 025 ff0 enhanceswhen augmenting sH values ff0 of sH 025 and 030 isfound to be very close bH 005 performs the friction lossaround 1ndash392 times above the smooth duct for sH 0ndash030and Re 100ndash2000

For 0le sHle 025 the pressure loss in the tested sectionaugments when enhancing sH at bH 010 sH 030 giveslower friction loss than sH 025 when Regt 600 In therange studies bH 010 performs the pressure loss higherthan the base case around 1ndash952 times depending on Re andsH values

(g)

Figure 8 Temperature contours in the y-z plane of the heat exchanger square duct installed with the 45deg ISR for (a) sH 0 (b) sH 005(c) sH 010 (d) sH 015 (e) sH 020 (f ) sH 025 and (g) sH 030 at BR 020 and Re 800


At bH 015 and 020 0le sHle 020 the friction lossincreases when improving the sH value ff0 is found to bearound 113ndash1715 and 147ndash2803 times over the smoothduct respectively for bH 015 and 020

In the range 0le sHle 010 at bH 025 the pressure lossaugments when inducing the sH value -e 45deg ISR with bH 025 brings the greater pressure loss around 215ndash4583times than the smooth duct

When increasing sH the pressure drop in the testedsection with the 45deg ISR at bH 030 reduces ff0 in thestudied section is about 340ndash6479 when inserting bH 030 of the 45deg ISR

-e variation of the TEF with the Reynolds number atvarious cases is presented as Figures 18(a)ndash18(f) respec-tively for the heating duct equipped with the 45deg ISR at bH 005 010 015 020 025 and 030 -e presence of the

sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20

Figure 9 Nux of the heat exchanger square duct installed with the 45deg ISR for BR 005 and Re 800

sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20



45deg ISR in the heat exchanger duct performs higher TEF thanthe smooth duct with no ISR (TEFgt 1) in almost cases -emaximum TEF in the range investigated is around 194 211223 245 284 and 252 for the heating section with the 45degISR at bH 005 010 015 020 025 and 030 respectively

-e relation of NuNu0 ff0 and TEF with sH for theheat exchanger duct at various bH and Re values is shown asFigures 19ndash21 respectively Considering Re 2000 the peakof heat transfer rate is detected at sH 005 030 025 015010 and 010 for the 45deg ISR with bH 005 010 015 020

025 and 030 respectively -e insertion of the 45deg ISR inthe studied section not only improves heat transfer rate butalso enhances pressure loss -e maximum pressure loss inthe tested section is found at s 30 25 20 20 15 and 15 ofthe duct height respectively for bH 005 010 015 020025 and 030 when considering Re 2000 Because theinstallation of the 45deg ISR in the tested duct brings greaterheat transfer rate and pressure loss than the smooth duct theTEF is selected to analyze the efficiency of the present testedsection-e greatest TEF is detected at sH around 005 030

sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )

Figure 16 NuNu0 versus Reynolds number for the heat exchanger square duct installed with the 45deg ISR at (a) bH 005 (b) bH 010 (c)bH 015 (d) bH 020 (e) bH 025 and (f) bH 030

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued


015 010 010 and 010 respectively for the square ductwith the 45deg ISR at bH around 005 010 015 020 025 and030

Figures 22(a) and 22(b) present the average NuNu0versus bH and average ff0 versus bH in the heat exchangerduct inserted with the 45deg ISR respectively e average

Nusselt number in the heat exchanger square duct insertedwith the 45deg ISR increases when augmenting the bH valueexcept for sH 020 and 025 e average Nusselt numberratio in the heat exchanger square duct inserted with the 45degISR slightly decreases when bHgt 025 and 020 for sH 020 and 025 respectively For sH 0 the 45deg ISR gives

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )

Figure 17 ff0 versus Reynolds number for the heat exchanger square duct installed with the 45deg ISR at (a) bH 005 (b) bH 010 (c) bH 015 (d) bH 020 (e) bH 025 and (f) bH 030


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )

Figure 18 TEF versus Reynolds number for the heat exchanger square duct installed with the 45deg ISR at (a) bH 005 (b) bH 010 (c) bH 015 (d) bH 020 (e) bH 025 and (f) bH 030

34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued


the average NuNu0 around 119 195 199 208 232 and277 respectively for bH 005 010 015 020 025 and030 At sH 005 the average Nusselt number is around188 196 211 247 307 and 390 greater than the smoothduct for bH 005 010 015 020 025 and 030 re-spectively e average NuNu0 is around 190 208 262

368 521 and 601 respectively for bH 005 010 015020 025 and 030 at sH 010 For sH 015 the averageNuNu0 is around 186 218 322 430 498 and 555respectively for bH 005 010 015 020 025 and 030e average NuNu0 is found to be around 182 242 349409 426 and 422 for bH 005 010 015 020 025 and

5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )

Figure 19 NuNu0 versus sH for the heat exchanger square duct installed with the 45deg ISR at (a) bH 005 (b) bH 010 (c) bH 015(d) bH 020 (e) bH 025 and (f) bH 030


000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )

Figure 20 ff0 versus sH for the heat exchanger square duct installed with the 45deg ISR at (a) bH 005 (b) bH 010 (c) bH 015 (d) bH 020 (e) bH 025 and (f) bH 030

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued


030 respectively at sH 020 e 45deg ISR with sH 025provides the average NuNu0 around 177 252 335 375and 365 for bH 005 010 015 020 and 025 respec-tively At sH 030 NuNu0 is around 173 254 305 and

321 respectively for bH 005 010 015 and 020 eaverage ff0 augments when enhancing bH for all sH valuesIn the range studies ff0 in the heat exchanger duct ttedwith the 45deg ISR is around 100ndash2825 100ndash4518

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )

Figure 21 TEF versus sH for the heat exchanger square duct installed with the 45deg ISR at (a) bH 005 (b) bH 010 (c) bH 015 (d) bH 020 (e) bH 025 and (f) bH 030


104ndash5957 115ndash6479 127ndash4629 134ndash3102 and142ndash1889 respectively for sH 0 005 010 015 020025 and 030

6 Conclusion

Numerical analysis on flow topology and heat transfer be-havior in the heat exchanger duct installed with 45deg ISR isreported -e influences on flow and heat transfer mecha-nisms for the ISR size and placement in the square duct areconsidered for laminar flow regime with the Reynoldsnumber around 100ndash2000 -e conclusions for the presentinvestigation are as follows

-e installation of the 45deg ISR in the tested sectionbrings higher pressure drop and heat transfer rate than thegeneral square duct for all tested cases In the range studiesthe Nusselt number and friction factor are around100ndash1005 and 100ndash6479 times over the general squareduct with no ISR respectively -e optimum thermal en-hancement factor for the present work is around 284 at bH 025 and sH 010

-e ISR size and placement effect changes both flow andheat transfer structures in the square duct -e difference of thesH and bH values changes the impinging position of the vortexflow on the duct walls and also reduces or increases the strengthof the vortex flow For the present research the suggestion forthe spacing between the outer edge of the ISR and the duct wallis around 010H with the recommendation of the ring heightaround 020ndash030H when considering the TEF value

In comparison the thermal enhancement factor for thepresent research is close to the thermal enhancement factorfrom [30] which presented the V-rib placed on the upper-lower walls of the square duct However the maintenanceproduction and installation of the current vortex generatorare easier than the previous work [30]

Nomenclature

B Ring height mDh Hydraulic diameter of channel mf Friction factors Gap spacing between the outer edge of the ISR

and duct walls mH Channel height mh Convective heat transfer coefficient Wmiddotmminus 2middotKminus 1

k -ermal conductivity Wmiddotmminus 1middotKminus 1

Nu Nusselt number (hDhk)P Pitch spacing mp Static pressure PaRe Reynolds numberT Temperature Kui Velocity in xi-direction mmiddotsminus 1

u Mean velocity in the channel mmiddotsminus 1

Greek letterTEF -ermal enhancement factor ((NuNu0)(ff0)13)ρ Density kgmiddotmminus 3

Subscript0 Smooth tubepp Pumping power

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this article

bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)

Figure 22 (a) AverageNuNu0 vs bH and (b) average ff0 vs bH for the heat exchanger square duct installed with the 45deg ISR at various sH values


Acknowledgments

-e authors would like to thank Assoc Prof Dr PongjetPromvonge for suggestions -is research was funded byCollege of Industrial Technology King Mongkutrsquos Uni-versity of Technology North Bangkok (Grant no Res-CIT02382019)

References

[1] M Bahiraei N Mazaheri Y Hosseini and H Moayedi ldquoAtwo-phase simulation for analyzing thermohydraulic per-formance of Cundashwater nanofluid within a square channelenhanced with 90deg V-shaped ribsrdquo International Journal ofHeat and Mass Transfer vol 145 Article ID 118612 2019

[2] W Bai D Liang W Chen and M K Chyu ldquoInvestigation ofribs disturbed entrance effect of heat transfer and pressuredrop in pin-fin arrayrdquo Applied ampermal Engineering vol 162Article ID 114214 2019

[3] GWang N Qian and G Ding ldquoHeat transfer enhancement inmicrochannel heat sink with bidirectional ribrdquo InternationalJournal of Heat and Mass Transfer vol 136 pp 597ndash609 2019

[4] P Liu J Lv F Shan Z Liu and W Liu ldquoEffects of rib ar-rangements on the performance of a parabolic trough receiverwith ribbed absorber tuberdquo Applied ampermal Engineeringvol 156 pp 1ndash13 2019

[5] Y Li Y Rao D Wang P Zhang and X Wu ldquoHeat transferand pressure loss of turbulent flow in channels with miniaturestructured ribs on one wallrdquo International Journal of Heat andMass Transfer vol 131 pp 584ndash593 2019

[6] W Bai W Chen L Yang and M K Chyu ldquoNumericalinvestigation on heat transfer and pressure drop of pin-finarray under the influence of rib turbulators induced vorticesrdquoInternational Journal of Heat and Mass Transfer vol 129pp 735ndash745 2019

[7] L Chai L Wang and X Bai ldquo-ermohydraulic performanceof microchannel heat sinks with triangular ribs on side-wallsmdashPart 1 local fluid flow and heat transfer characteris-ticsrdquo International Journal of Heat and Mass Transfervol 127 pp 1124ndash1137 2018

[8] L Chai L Wang and X Bai ldquo-ermohydraulic performanceof microchannel heat sinks with triangular ribs on side-wallsmdashPart 2 average fluid flow and heat transfer charac-teristicsrdquo International Journal of Heat and Mass Transfervol 128 pp 634ndash648 2019

[9] X Cao T Du Z Liu H Zhai and Z Duan ldquoExperimentaland numerical investigation on heat transfer and fluid flowperformance of sextant helical baffle heat exchangersrdquo In-ternational Journal of Heat andMass Transfer vol 142 ArticleID 118437 2019

[10] A A A Arani and R Moradi ldquoShell and tube heat exchangeroptimization using new baffle and tube configurationrdquo Ap-plied ampermal Engineering vol 157 Article ID 113736 2019

[11] M A Ismael ldquoForced convection in partially compliantchannel with two alternated bafflesrdquo International Journal ofHeat and Mass Transfer vol 142 Article ID 118455 2019

[12] E M S El-Said and M M A Al-Sood ldquoShell and tube heatexchanger with new segmental baffles configurations acomparative experimental investigationrdquo Applied ampermalEngineering vol 150 pp 803ndash810 2019

[13] SW Chang TW Chen and YW Chen ldquoDetailed heat transferand friction factor measurements for square channel enhanced byplate insert with inclined baffles and perforated slotsrdquo Appliedampermal Engineering vol 159 Article ID 113856 2019

[14] A J Modi and M K Rathod ldquoComparative study of heattransfer enhancement and pressure drop for fin-and-circulartube compact heat exchangers with sinusoidal wavy and el-liptical curved rectangular winglet vortex generatorrdquo Inter-national Journal of Heat and Mass Transfer vol 141pp 310ndash326 2019

[15] H Kobayashi K Yaji S Yamasaki and K Fujita ldquoFreeformwinglet design of fin-and-tube heat exchangers guided bytopology optimizationrdquo Applied ampermal Engineeringvol 161 Article ID 114020 2019

[16] H-l Liu C-c Fan Y-l He and D S Nobes ldquoHeat transferand flow characteristics in a rectangular channel with com-bined delta winglet insertsrdquo International Journal of Heat andMass Transfer vol 134 pp 149ndash165 2019

[17] C Zhai M D Islam R Simmons and I Barsoum ldquoHeattransfer augmentation in a circular tube with delta wingletvortex generator pairsrdquo International Journal of ampermalSciences vol 140 pp 480ndash490 2019

[18] M F M Salleh H A Mohammed and M A Wahidldquo-ermal and hydraulic characteristics of trapezoidal wingletacross fin-and-tube heat exchanger (FTHE)rdquoAppliedampermalEngineering vol 149 pp 1379ndash1393 2019

[19] G LiangM D Islam N Kharoua and R Simmons ldquoNumericalstudy of heat transfer and flow behavior in a circular tube fittedwith varying arrays of winglet vortex generatorsrdquo InternationalJournal of ampermal Sciences vol 134 pp 54ndash65 2018

[20] S Chamoli R Lu J Xie and P Yu ldquoNumerical study on flowstructure and heat transfer in a circular tube integrated withnovel anchor shaped insertsrdquo Applied ampermal Engineeringvol 135 pp 304ndash324 2018

[21] A Bartwal A Gautam M Kumar C K Mangrulkar andS Chamoli ldquo-ermal performance intensification of acircular heat exchanger tube integrated with compoundcircular ring-metal wire net insertsrdquo Chemical Engineeringand Processing-Process Intensification vol 124 pp 50ndash702018

[22] S Chamoli R Lu D Xu and P Yu ldquo-ermal performanceimprovement of a solar air heater fitted with winglet vortexgeneratorsrdquo Solar Energy vol 159 pp 966ndash983 2018

[23] S K SinghM Kumar A Kumar A Gautam and S Chamolildquo-ermal and friction characteristics of a circular tube fittedwith perforated hollow circular cylinder insertsrdquo Appliedampermal Engineering vol 130 pp 230ndash241 2018

[24] S Chamoli R Lu and P Yu ldquo-ermal characteristic of aturbulent flow through a circular tube fitted with perforatedvortex generator insertsrdquo Applied ampermal Engineeringvol 121 pp 1117ndash1134 2017

[25] S Chamoli P Yu and S Yu ldquoMulti-objective shape opti-mization of a heat exchanger tube fitted with compoundinsertsrdquo Applied ampermal Engineering vol 117 pp 708ndash7242017

[26] J S Sawhney R Maithani and S Chamoli ldquoExperimentalinvestigation of heat transfer and friction factor characteristicsof solar air heater using wavy delta wingletsrdquo AppliedampermalEngineering vol 117 pp 740ndash751 2017

[27] S V Patankar C H Liu and E M Sparrow ldquoFully developedflow and heat transfer in ducts having streamwise-periodicvariations of cross-sectional areardquo Journal of Heat Transfervol 99 no 2 pp 180ndash186 1977

[28] P Promvonge W Jedsadaratanachai S Kwankaomeng andC -ianpong ldquo3D simulation of laminar flow and heattransfer in V-baffled square channelrdquo International Com-munications in Heat and Mass Transfer vol 39 no 1pp 85ndash93 2012


[29] Y Cengel and A J Ghajar Heat and Mass Transfer Funda-mentals amp Applications ISBN 978-981-4595-27-8 McGraw-Hill Education Newyork NY USA 5th edition 2015

[30] A Boonloi and W Jedsadaratanachai ldquoEffect of location intransverse plane for 45-degree V-baffle on flow and heattransfer mechanism in a square channelrdquo Frontiers in Heatand Mass Transfer vol 11 no 29 2018


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Submit your manuscripts atwwwhindawicom

heat transfer in the heat exchanger is greater than thesmooth tube around 335 times while the maximumthermal performance is around 284 Chamoli et al [22]presented the thermal performance of a solar air heaterplaced with the winglet vortex generator -e effects of tipedge ratio and flow attack angle for the winglet on heattransfer pressure loss and performance were studied forRe 3500ndash16000 -ey claimed the winglet vortex gen-erator in the heat exchanger gives the best thermalperformance in the range 172ndash220 Singh et al [23]studied the influences of the perforated hollow circularcylinder in a circular tube for Re 6000ndash27000 -eyfound that the perforated hollow circular cylinder in thecircular tube provides the heat transfer rate around150ndash230 when compared with the smooth tube Cha-moli et al [24] illustrated the convective heat transfer in acircular tube fitted with perforated vortex generators -eeffects of the perforation index and relative pitch lengthon heat transfer and thermal performance in the testedtube were considered for Re 3000ndash21000 -ey foundthat the circular tube with perforated vortex generatorsprovides the maximum thermal enhancement factoraround 165 -e multiobjective shape optimization of aheat exchanger tube fitted with compound inserts wasreported by Chamoli et al [25] Sawhney et al [26] ex-perimentally examined the heat transfer and frictionfactor in a solar air heater duct with wavy delta wingletsfor the Reynolds number around 4000ndash17300 -enumber of wave and relative longitudinal pitch for thewavy delta winglet was compared -ey claimed that thewavy delta winglet in the duct performs the heat transferrate greater than the plain duct around 223

-e objective for the present research is to design thevortex generator with the special conditions as follows

(i) -e new design has high effectiveness to increaseheat transfer rate in the heat exchanger section

(ii) -e installation and maintenance of the vortexgenerator in the heat exchanger are stable andconvenient

(iii) -e production of the vortex generator is notcomplicated

In the present research the passive method is focused-e inclined square ring (ISR) like the baffle or thin rib isselected to improve heat transfer rate and performance inthe heat exchanger square duct -e parameter of the ISRand placement in the heating duct is investigated nu-merically in three dimensions-e numerical investigationmay help to describe the flow and heat transfer structuresin the heating section -e understanding on flow and heattransfer behaviors in the heat exchanger is an importantfactor for the development of the compact heat exchanger-e numerical study also saves the cost and resource forthe studied process when compared with the experimentalexamination -e numerical results are plotted in terms offlow and heat transfer configurations in the tested sectionsuch as temperature contour Nux Contour and stream-lines-e performance analysis in form of Nusselt number

friction factor and thermal enhancement factor for theheat exchanger square duct equipped with ISR is alsoconcluded

2 Tested Section with 45deg ISR

-e computational domain of the heat exchanger squareduct inserted with the 45deg ISR is plotted in Figure 1 -ephysical domain of the square duct inserted with the 45degISR in y-z plane is depicted as Figure 2 -e height of thesquare ductH is around 005m-e duct height is equal tothe hydraulic diameter or HDh -e ISRs are inserted inthe square duct with single pitch spacing ratio of 1 (PH 1) in all investigated cases -e ratio between the ISRheight b and channel height H or bH is varied in therange 005ndash030 -e spacing between the outer edge of theISR and the channel wall s is varied in terms of spacingratio or sH 0ndash030 -e air flow rate is presented in theform of Reynolds number -e Reynolds number at theinlet condition around 100ndash2000 is considered for thecurrent work -e numerical models with the mesh of theheat exchanger square duct inserted with the 45deg ISR areillustrated as Figures 3(a) and 3(b) for sH 0 and 020respectively at bH 020

3 Numerical Method

-e flow is a laminar regime with the Reynolds numberbased on the hydraulic diameter -e flow and heat transferare steady in three dimensions -e tested fluid is set asincompressible flow -e tested fluid is air with the Prandtlnumber around 0707 (300K) -e thermal properties of theair are counted to be constant at the average bulk meantemperature -e heat transfer in the force convection modeis considered for the present work while the radiation andnatural convection are ignored -e body force and viscousdissipation are also disregarded No slip wall condition isapplied for all channel surfaces and ISR -e periodiccondition [27] on both flow and heat transfer is applied forthe inlet and outlet of the computational domain -e ISR isassumed to be an insulator while the duct walls are set withconstant temperature around 310K -e flow and heattransfer in the heat exchanger duct fitted with the ISR are infully developed condition [28]

-e finite volume with the SIMPLE algorithm is selectedto solve the present investigation -e present model isanswered by the continuity the NavierndashStokes equationsand the energy equation which are illustrated as equations(1)ndash(3) respectively -e continuity equation momentumequation and energy equation are discretized by the powerlaw scheme power law scheme and QUICK scheme re-spectively -e numerical solutions are considered to beconverged when the normalized residual values are less than10minus 5 for all variables but less than 10minus 9 only for the energyequation

Continuity equation

z

zxi

ρui( 1113857 0 (1)


Inclined ring

Inclined ring



bH = sH = 020

Inclined ring

Channel wall

Flow direction

Flow direction

s

b

P

P

yxz

H = D h

y

xz

yxz


bH = 010

bH = 015

bH = 020

bH = 025

bH = 030

0 005 010 015 020 025 030sH

bH = 005

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z



Momentum equation

z ρuiuj1113872 1113873

zxj

minuszp

zxi

+z

zxj

μzui

zxj

+zuj

zxi

1113888 11138891113890 1113891 (2)

Energy equation

z

zxi

ρuiT( 1113857 z

zxj

ΓzT

zxj

1113888 1113889 (3)


Γ μPr

(4)


Re ρuDh

μ (5)


f (ΔPL)Dh

(12)ρu2 (6)


Nux hxDh

k (7)

Nu 1L

1113946Nuxzx (8)



TEF h

h0

11138681113868111386811138681113868111386811138681113868ppNuNu0

11138681113868111386811138681113868111386811138681113868pp

NuNu0( 1113857

ff0( 111385713 (9)





5 Numerical Result


yxz

(a)

yxz

(b)







Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Nu

Nu 0

0

1

2

3

4

5

6

7

8

bH = sH = 020



(a)

ff0

02468

1012141618202224262830

bH = sH = 020

Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200



(b)


Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

f0

00

01

02

03

04

05

06

07

Nu 0

26

28

30

32

34





yxz

(a)

yxz

(b)y

xz

(c)

yxz

(d)y

xz

(e)

yxz

(f)y

xz

(g)



Main vortex core

Main vortexcore

Small vortices


(a) (b)

(c) (d)

(e) (f )

Figure 8 Continued














(g)







sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Inclined ring

Inclined ring



bH = sH = 020

Inclined ring

Channel wall

Flow direction

Flow direction

s

b

P

P

yxz

H = D h

y

xz

yxz


bH = 010

bH = 015

bH = 020

bH = 025

bH = 030

0 005 010 015 020 025 030sH

bH = 005

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z

x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z x

y

z



Momentum equation

z ρuiuj1113872 1113873

zxj

minuszp

zxi

+z

zxj

μzui

zxj

+zuj

zxi

1113888 11138891113890 1113891 (2)

Energy equation

z

zxi

ρuiT( 1113857 z

zxj

ΓzT

zxj

1113888 1113889 (3)


Γ μPr

(4)


Re ρuDh

μ (5)


f (ΔPL)Dh

(12)ρu2 (6)


Nux hxDh

k (7)

Nu 1L

1113946Nuxzx (8)



TEF h

h0

11138681113868111386811138681113868111386811138681113868ppNuNu0

11138681113868111386811138681113868111386811138681113868pp

NuNu0( 1113857

ff0( 111385713 (9)





5 Numerical Result


yxz

(a)

yxz

(b)







Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Nu

Nu 0

0

1

2

3

4

5

6

7

8

bH = sH = 020



(a)

ff0

02468

1012141618202224262830

bH = sH = 020

Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200



(b)


Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

f0

00

01

02

03

04

05

06

07

Nu 0

26

28

30

32

34





yxz

(a)

yxz

(b)y

xz

(c)

yxz

(d)y

xz

(e)

yxz

(f)y

xz

(g)



Main vortex core

Main vortexcore

Small vortices


(a) (b)

(c) (d)

(e) (f )

Figure 8 Continued














(g)







sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Momentum equation

z ρuiuj1113872 1113873

zxj

minuszp

zxi

+z

zxj

μzui

zxj

+zuj

zxi

1113888 11138891113890 1113891 (2)

Energy equation

z

zxi

ρuiT( 1113857 z

zxj

ΓzT

zxj

1113888 1113889 (3)


Γ μPr

(4)


Re ρuDh

μ (5)


f (ΔPL)Dh

(12)ρu2 (6)


Nux hxDh

k (7)

Nu 1L

1113946Nuxzx (8)



TEF h

h0

11138681113868111386811138681113868111386811138681113868ppNuNu0

11138681113868111386811138681113868111386811138681113868pp

NuNu0( 1113857

ff0( 111385713 (9)





5 Numerical Result


yxz

(a)

yxz

(b)







Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Nu

Nu 0

0

1

2

3

4

5

6

7

8

bH = sH = 020



(a)

ff0

02468

1012141618202224262830

bH = sH = 020

Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200



(b)


Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

f0

00

01

02

03

04

05

06

07

Nu 0

26

28

30

32

34





yxz

(a)

yxz

(b)y

xz

(c)

yxz

(d)y

xz

(e)

yxz

(f)y

xz

(g)



Main vortex core

Main vortexcore

Small vortices


(a) (b)

(c) (d)

(e) (f )

Figure 8 Continued














(g)







sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Nu

Nu 0

0

1

2

3

4

5

6

7

8

bH = sH = 020



(a)

ff0

02468

1012141618202224262830

bH = sH = 020

Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200



(b)


Re0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

f0

00

01

02

03

04

05

06

07

Nu 0

26

28

30

32

34





yxz

(a)

yxz

(b)y

xz

(c)

yxz

(d)y

xz

(e)

yxz

(f)y

xz

(g)



Main vortex core

Main vortexcore

Small vortices


(a) (b)

(c) (d)

(e) (f )

Figure 8 Continued














(g)







sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


yxz

(a)

yxz

(b)y

xz

(c)

yxz

(d)y

xz

(e)

yxz

(f)y

xz

(g)



Main vortex core

Main vortexcore

Small vortices


(a) (b)

(c) (d)

(e) (f )

Figure 8 Continued














(g)







sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Main vortex core

Main vortexcore

Small vortices


(a) (b)

(c) (d)

(e) (f )

Figure 8 Continued














(g)







sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














(g)







sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20






sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





sH = 0 sH = 005 sH = 010 sH = 015

sH = 020 sH = 025 sH = 030

Nusselt number 0 20


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020 sH = 025

Nusselt number 0 30


sH = 0 sH = 005 sH = 010

sH = 015 sH = 020

Nusselt number 0 30



WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


WallA

WallB

WallC

WallD

Figure 15 Wall code

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 005

(a)

Nu

Nu 0

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 010

(b)

Nu

Nu 0

60

55

50

45

40

35

30

25

20

15

10

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 015

(c)

Nu

Nu 0

6055504540353025201510

80757065

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

(d)

Figure 16 Continued


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Nu

Nu 0

6055504540353025201510

80757065

110105100

959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

bH = 025

(e)

Nu

Nu 0 60

55504540353025201510

80757065

100959085

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

bH = 030

(f )


Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

45

40

35

30

25

20

15

10

ff0

bH = 005

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

10

8

6

4

2

ff0

bH = 010

(b)

Figure 17 Continued





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

18

16

14

12

10

8

6

4

2

ff0

bH = 015

(c)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

30

25

20

15

10

5

ff0

bH = 020

(d)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

50

40

30

20

10

ff0

bH = 025

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 22002000

sH = 0sH = 005sH = 010

sH = 015sH = 020

70

60

50

40

30

20

10

ff0

bH = 030

(f )



Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 00522

20

18

16

14

12

10

08

TEF

(a)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 01022

20

18

16

14

12

10

08

TEF

(b)

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

2000

bH = 015

TEF

(c)

26

24

22

20

18

16

14

12

10

08

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

bH = 020

2000

TEF

(d)

Figure 18 Continued


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020sH = 025

2000

bH = 025

TEF

30

25

20

15

10

(e)

Re0 200 400 600 800 1000 1200 1400 1600 1800 2200

sH = 0sH = 005sH = 010

sH = 015sH = 020

2000

TEF

28

26

24

22

20

18

16

14

12

10

08

bH = 030

(f )


34

32

30

28

26

24

22

20

18

16

14

12

10

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 005

(a)

52

48

44

40

36

32

28

24

20

16

12

08

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

(b)

Figure 19 Continued




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




5248444036322824201612

0408

646056

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 015

(c)

524844403632282420161208

646056

80767268

Nu

Nu 0

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 020

(d)

11

10

9

8

7

6

5

4

3

2

1

0

Nu

Nu 0

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

(e)

11

10

9

8

7

6

5

4

3

2

1

Nu

Nu 0

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 030

(f )



000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

40

35

30

25

20

15

10

ff0

bH = 005

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

10

9

8

7

6

5

4

3

2

1

ff0

bH = 010

(b)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

181716151413121110

987654321

ff0

bH = 015

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

323028262422201816141210

8642

ff0

bH = 020

(d)

Figure 20 Continued


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

50

45

40

35

30

25

20

15

10

5

ff0

bH = 025

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

70

65

60

55

50

45

40

35

30

25

20

15

10

5

ff0

bH = 030

(f )


000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

030 035

bH = 005

20

18

16

14

12

10

TEF

Re = 1200Re = 1600Re = 2000

(a)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 010

20

18

16

14

12

10

24

22

08

TEF

(b)

Figure 21 Continued




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 01524

22

20

18

16

14

12

10

08

TEF

(c)

000 005 010 015 020 025 030 035sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 02024

22

20

18

16

14

12

10

08

26

TEF

(d)

000 005 010 015 020 025 030sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 025

24

22

20

18

16

14

12

10

08

30

28

26

TEF

(e)

000 005 010 015 020 025sH

Re = 100Re = 200Re = 400

Re = 600Re = 800Re = 1000

Re = 1200Re = 1600Re = 2000

bH = 03024

22

20

18

16

14

12

10

08

26

TEF

(f )




6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



6 Conclusion





Nomenclature








Data Availability




bH000 005 010 015 020 025 030 035

Ave

rage

Nu

Nu 0

0

1

2

3

4

5

6

7

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(a)

bH000 005 010 015 020 025 030 035

0

5

10

15

20

25

30

35

Ave

rage

ff 0

sH = 0sH = 005sH = 010

sH = 015sH = 020

sH = 025sH = 030

(b)



Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Acknowledgments


References



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


thermohydraulic performance improvement in heat exchanger

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