international journal heat mass transfertsl.energy.hust.edu.cn/2021_cuihaichuan_01.pdfh.c. cui, x.t....

International Journal of Heat and Mass Transfer 167 (2021) 120839

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer

journal homepage: www.elsevier.com/locate/hmt

Overall numerical simulation and experimental study of a hybrid

oblique-rib and submerged jet impingement/microchannel heat sink

H.C. Cui, X.T. Lai, J.F. Wu, M.Z. Wang, W. Liu ∗, Z.C. Liu ∗

School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

a r t i c l e i n f o

Article history:

Received 16 July 2020

Revised 15 November 2020

Accepted 16 December 2020

Keywords:

Hybrid heat sink

Oblique-rib

Microchannel and jet

Rib arrangement

Impingement

Overall numerical simulation

a b s t r a c t

In this work, two submerged jet impingement/microchannel heat sink (JIMHS) models were pro-

posed, i.e., straight-rib jet impingement/microchannel heat sink (SJIMHS) and oblique-rib jet impinge-

ment/microchannel heat sink (OJIMHS). The heat transfer and flow characteristics of the two models were

investigated by overall numerical simulation and experiment. In the numerical simulation, the effects of

heat flux, pressure drop and rib arrangement on the internal flow and heat transfer of the heat sink were

studied. The results indicate that under the same heat flux and inlet condition, the heat transfer surface

of OJIMHS achieves more uniform and lower temperature distribution compared with that of SJIMHS, and

the average convective heat transfer coefficient of the OJIMHS is obviously higher than that of SJIMHS in

all calculation cases, with an increase of about 20%. In addition, the performance of OJIMHS was tested

experimentally. The comparison indicates that the maximum relative errors of average temperature and

heat transfer coefficient between simulation and experiment were less than 9%. When the volume flow

rate is 0.5 L/min and the heat flux is 100 W/cm ², the average temperature of the heat transfer surface is still lower than 60 °C. Besides, the averaged heat transfer coefficient of 2.8 W / ( cm 2 · K) was achieved under the inlet fluid temperature of 283K and volume flow rate of 2.5 L/min in the experiment.

© 2020 Elsevier Ltd. All rights reserved.

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. Introduction

With the continuous progress of information technology and

icromachining technology, most of electronics are developing in

he direction of miniaturization. However, the problem of heat

issipation with high heat flux has become a major obstacle to

he development of electronics in the future [1–3] . According to

oore’s law, the number of transistors in dense integrated circuits

ncreases exponentially [4] . As the number increases, the heat flux

n electronics can reach 100 W / c m 2 [5] . Faced with such high heat

ux, most of the conventional cooling methods have failed [6] .

n comparison, jet impingement/microchannel cooling technology,

hich combines the advantages of microchannel cooling and jet

mpingement cooling technology, has been proved to be capable

o afford high heat flux cooling capacity by simulation and experi-

ent in recent years [7–12] .

Abbreviations: EMF, electromagnetic flowmeter; GCI, grid convergence in-

ex; ORP, oblique ribbed plate; SRP, straight ribbed plate; SJIMHS, straight-

ib jet impingement/microchannel heat sink; OJIMHS, oblique-rib jet impinge-

ent/microchannel heat sink. ∗ Corresponding authors.

E-mail addresses: [email protected] (W. Liu), [email protected] (Z.C. Liu).

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ttps://doi.org/10.1016/j.ijheatmasstransfer.2020.120839

017-9310/© 2020 Elsevier Ltd. All rights reserved.

Microchannel heat sink has been widely used in the heat dis-

ipation of some high heat flux electronics because of its high ef-

ciency and compact structure. Tuckerman and Pease introduced

he concept of microchannel heat sink for the first time in 1981,

nd indicated that this method can significantly reduce heat trans-

er resistance and then enhance heat transfer [13] . In the following

ecades, a lot of experiments and simulations have been carried

ut to optimize the shape of microchannel, the internal structure

nd the flow pattern of the heat sink. Xia et al. studied the heat

ransfer and flow characteristics of complex wave-like microchan-

el heat sink by experiment and numerical simulation, and com-

ared with the rectangular microchannel heat sink. The results in-

icate that the heat transfer performance of the complex wavy-like

icrochannel heat sink is better than that of the traditional rect-

ngular microchannel heat sink [14] . Deng et al. compared the heat

ransfer performance of � − shape reentrant microchannel heat ink and rectangular microchannel heat sink under different work-

ng fluids, deionized water and ethanol, experimentally. The results

how that the reentrant microchannels give a better heat transfer

erformance for both coolants tests [15] . Zhai et al. investigated

he effect of parallel flow, counter flow and different channel ge-

metries on the heat transfer performance of the double-layered

icrochannel heat sink by three-dimension method. The results

ndicate that the double-layered microchannel heat sink with dif-

https://doi.org/10.1016/j.ijheatmasstransfer.2020.120839http://www.ScienceDirect.comhttp://www.elsevier.com/locate/hmthttp://crossmark.crossref.org/dialog/?doi=10.1016/j.ijheatmasstransfer.2020.120839&domain=pdfmailto:[email protected]:[email protected]://doi.org/10.1016/j.ijheatmasstransfer.2020.120839

H.C. Cui, X.T. Lai, J.F. Wu et al. International Journal of Heat and Mass Transfer 167 (2021) 120839

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Nomenclature

A 1 , A 2 the area of the bottom heating surface and heat

transfer surface respectively ( m 2 )

C 1 ε , C 2 ε constants for RNG k − ε model c p specific heat at constant pressure ( J · k g −1 · K −1 ) D diameter(m)

h, h heat transfer coefficient and the average heat trans-

fer coefficient, respectively ( W · c m −2 · K −1 ) H height(m)

k thermal conductivity ( W · c m −2 · K −1 ) or turbulence kinetic energy(J)

L length (m)

˙ m coolant mass flow rate ( kg · s −1 ) N the number of grid

P pressure (Pa)

Q the heating power(W)

q heat flux of the bottom heating surface ( W · c m −2 ) Re Reynolds number

T , T temperature and the average temperature, respec-

tively (K, °C) u, v , w velocity ( m · s −1 ) W width ( m )

Zn jet-to-surface space ratio

Greek symbols

ρ density ( kg · m −3 ) ε dissipation rate of turbulence kinetic energy λ thermal conductivity ( W · m −1 · K −1 ) μ dynamic viscosity ( Pa · s ) ηt eddy viscosity coefficient σε , σk turbulent Prandtl numbers for k and ε

Subscript

a v laterally-averaged f average value of inlet and outlet

in the heat sink inlet

jet jet hole

max maximum value

min minimum value

w the bottom heat transfer surface

out the heat sink outlet

erent channel geometries in each layer has a better heat trans-

er performance and lower pressure drop [16] . Although the mi-

rochannel heat sink can realize high heat flux dissipation by in-

reasing heat transfer area or enhancing disturbance [14] , the large

ressure and temperature gradient along the flow direction have

ecome the main obstacles restricting its application [ 13 , 17 ].

As for jet impingement cooling technology, due to the ex-

remely thin velocity and temperature boundary layer formed after

he high-speed fluid impinges on the heat transfer surface [ 18 , 19 ],

very high convective heat transfer coefficient will be generated in

he stagnation zone of jet. In addition, compared with microchan-

el cooling technology, jet impingement cooling technology has a

maller pressure loss [17] . As a consequence, the jet impingement

ooling technology is considered to be one of the most potential

eans to deal with the problem of heat dissipation with high heat

ux and has attracted extensive attention from scholars [20] . Wang

t al. studied the single-hole jet and jet array by three-dimensional

umerical simulation and experimental method, and compared the

ffects of jet orifice diameter and the number of jet orifices on

ooling effect [21] . Since the heat transfer coefficient will drop

harply away from the stagnation point, the application of jet ar-

ay is more common in the field of electronics heat dissipation

2

22 , 23 ]. McInturff et al. investigated the effect of hole shape on im-

ingement jet array heat transfer by experimental method. The test

as conducted under the jet Reynolds numbers of 90 0, 150 0,50 0 0,

nd 11,0 0 0 and the results show that the racetrack hole config-

ration generally provides approximately the same heat transfer

ugmentation as the circle hole configuration, with slightly better

erformance, under some conditions. The triangle hole configura-

ion provides lower heat transfer augmentation, compared to both

he circle hole and racetrack hole configurations [24] . Parida et al.

tudied the effect of wall-integrated inclined impingement jets in

confined environment by numerical simulation and experimental

ethod. The results show that by tilting the jet hole to a certain

ngle, two asymmetric secondary flow regions can be formed in

he channel under the interaction of jet and the wall. Due to the

econdary flow region, the jets get accelerated and flow out at rel-

tively higher velocity causing the heat transfer rates to increase

ocally [25] .

Compared with microchannel cooling technology and jet

mpingement cooling technology, jet impingement/microchannel

ooling technology was expected to have better heat transfer per-

ormance due to integrating the advantages of two technologies.

ung et al. used simulation and experimental method to study

he cooling performance of JIMHS with HFE-7100 as working fluid.

he results show that the heat conduction along the side wall of

he microchannel is particularly significant in the single-phase re-

ion at relatively low jet velocity, and the temperature gradient

long the microchannel decreases with increasing the height of

he microchannel at relatively low jet velocity [26] . In addition,

ung et al. also studied the effects of jet sizes and jet array pat-

erns on the heat transfer performance of JIMHS. They found that

he decreasing-jet-size pattern yields the highest convective heat

ransfer coefficients and lowest wall temperatures, while the equal-

et-size pattern provides the greatest uniformity in wall temper-

ture [17] . To further improve the heat transfer performance of

IMHS, some scholars propose to introduce passive structures in

he microchannels [27–33] . Husain et al. used numerical simula-

ion to study the effect of adding pillar structure on heat trans-

er performance. The results show that pillars in the channel con-

ributed to enhanced heat transfer coefficient and higher heat

ransfer coefficient can be achieved with smaller jet-to-jet pitch

atio, while lower pressure drop can be achieved with larger jet-

o-jet pitch ratio [30] . Huang et al. carried out a three-dimensional

umerical simulation to study the heat transfer performance of

IMHS by introducing the dimples to heat transfer surface. The

imulation results indicate that JIMHS with convex dimples exhib-

ted the best cooling performance. In addition, they further studied

he effect of the positional distribution of the dimples on the heat

ransfer performance and pressure drop [31–33] .

According to above literature research, it can be noticed that

or microchannel cooling technology, special microchannel struc-

ure can enhance the heat transfer performance by increasing heat

ransfer area and enhancing disturbance, but the disadvantages are

hat there is often a large pressure gradient along the flow direc-

ion, and the temperature distribution of the heat transfer surface

s not uniform [ 13 , 17 ]. As for jet cooling technology, the advan-

ages are that the extremely high convective heat transfer coeffi-

ient can be obtained in stagnation zone and the better synergy

f temperature field and velocity field [34–36] , but the disadvan-

age is that the heat transfer coefficient will decrease sharply af-

er leaving the stagnation zone. Therefore, many scholars propose

o combine microchannel cooling technology with jet array cool-

ng to complement each other and design the novel jet impinge-

ent/microchannel heat sink to meet the needs of high heat flux

issipation. However, the research in this field mainly focuses on

umerical simulation of a symmetrical unit or a single channel of

he heat sink [ 17 , 30 , 31 ], and the overall simulation is less. Accord-


Fig. 1. (a) Assembly diagram of experimental testing system; (b) system loop physical map; (c) distribution of temperature measuring points.

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ng to the numerical simulation results, the analysis of the whole

erformance of heat sink and the essence of flow and heat transfer

echanism is relatively less. In this work, two different submerged

et impingement/microchannel heat sink models were proposed,

nd the heat transfer and flow characteristic were systematically

nvestigated from the aspect of overall numerical simulation and

xperiment.

. Experimental verification

.1. Introduction of experimental system

Fig. 1 shows the schematic diagram and physical map of the

xperimental circuit with deionized water as cooling fluid. The ex-

erimental system is mainly composed of two parts, one is the

ystem components, and the other is the measuring and control

omponents. The system components of the experimental circuit

re liquid accumulator, micropump, jet impingement/microchannel

eat sink, heat source, condensation device, valves and pipes be-

ween the components. Measuring and control components mainly

nclude electromagnetic flowmeter (EMF), pressure gauge, power

eter, thermocouple and SSR (solid state relay).

.2. Introduction of main system components

.2.1. Jet impingement/microchannel heat sink

As shown in the Fig. 2 , the novel JIMHS consists of three parts:

he top jet orifice plate, the frame and the heat transfer rib plate.

he material of the heat sink is cooper, which is processed by

achine tools and EDM. Looking at Fig. 2 (a), unlike the three-

imensional model shown in Fig. 6 , there are raised rectangular

ibs above the plate, which is used to enhance the mechanical

roperties of the jet orifice plate and prevent the plate from de-

3

orming under pressure. In addition, the dimensional parameters

f the heat sink can be found in Fig. 6 and Table 2 .

.2.2. Heat source

Fig. 3 shows the physical map and three-dimensional perspec-

ive view of the heat source. The material of heat source is copper,

hich is cut and processed by machine tools. There are 16 process-

ng holes at the bottom, corresponding to 16 heating rods inserted.

he maximum power provided by each heating rod is 100 W. Four

oles of different lengths with diameter of 1 mm were machined

t the upper part near 5 mm of the contact surface for inserting

hermocouples to measure the temperature of the heat source. The

ontact area between heat source and heat sink is 40 × 20 mm ². he contact surface is smooth and coated with a layer of heat con-

ucting paste. After that, the heat source and heat sink are tightly

dhered and fixed with screws.

.3. Introduction of measuring components

The relevant parameters of measuring components and gear

ump are shown in Table 1 .

.4. Experimental data measurement

.4.1. Temperature measurement and flow measurement

In the experiment, the T-type thermocouples were used for

emperature measurement, in which the measurement error is

0.2 °C. A total of 10 temperature measuring points were arranged n the experiment. Four of the temperature measuring points are

rranged around the heat sink and placed close to the heat sink

all for temperature measurement and the average of the mea-

ured values approximately replaces the average temperature of

he heat transfer surface, like the T 5 and T 6 in Fig. 1 (c). In ad-

ition, T and T are in the symmetrical position. The other four

7 8


Fig. 2. (a) Top jet orifice plate(front); (b) top jet orifice plate(back); (c) frame and heat transfer rib plate.

Fig. 3. (a) Physical diagram of the heat source; (b) the three-dimensional perspec-

tive diagram of the heat source.

Table 1

Specification parameters of system measuring components.

Component name Specifications and parameters

Gear pump Model number: MG317XK/DC24W

Electromagnetic flowmeter Model number: AXG005G, Range: 0-3 L/min

Pressure gage FUJI, Range: 30-3000 KPa, -0.1-0.2 MPa

Power meter Model number: PF9800, accuracy class: 0.5

Data collector Model number: Keithley-2700

Direct-current main 24 V

Voltage regulating transformer Model number: TDGC-0.5

Fixed resistance 4 × 250 �Solid state relay Model number: GJH3-80A

Thermocouple T-type thermocouple, ±0.2 °C

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emperature measuring points are arranged at the upper part of

he heating source close to the contact surface by 5 mm, as shown

n Figs. 1 (c) and 3 . The depths of the four measuring points are

, 10, 12 and 15 mm, respectively. The remaining two temperature

easuring points are respectively arranged inside the liquid accu-

ulator and at the outlet pipe wall for measuring the inlet and

utlet temperatures of the heat sink.

The flowmeter shown in Fig. 1 is an electromagnetic flowmeter

EMF) used in this experiment to measure the overall flow into the

eat sink. The measurement range of the flowmeter is 0-3 L/min,

hich is connected in series to the whole circuit of the system.

.5. Experimental conditions

In the experiment, the inlet temperature was constant at

0 ±0.4 °C. The testing volume flow rate was 0.5 L/min, 0.75 L/min, L/min, 1.25 L/min, 1.5 L/min, 1.75 L/min, 2 L/min, 2.25 L/min and

.5 L/min, respectively. Nine different heat fluxes were test at each

olume flow rate, and increased from the lowest 20 W / c m 2 to 100

/ c m 2 with a step increment of 10 W / c m 2 .

4

.6. Data reduction and uncertainty analysis

Assuming that the physical properties of the deionized water

irculating in the experimental system remain constant with the

umber of tests, the average heat flux absorbed by the heat sink

an be calculated by the heat absorption formula of water:

= c p ˙ m ( T out − T in ) (1) here c p is the specific heat capacity of water, and T in and T out are

he inlet and outlet temperature of the heat sink, respectively.

The average temperature of the heat transfer surface can be es-

imated by the following formula:

= 1 4

8 ∑ i =5

T i (2)

here T 5 ~T 8 are the external surface temperatures of the heat sink

ottom.

The average convective heat transfer coefficient ( h ) is defined

s:

= Q A 2 ( T − T f )

(3)

Among them, T f is the average temperature of the heat sink

nlet and outlet and A 2 is the area of the heat transfer surface.

As shown in Table 1 , the absolute error of the T-type ther-

ocouple is ±0.2 °C, and the relative error of the electromagnetic owmeter is ±1% . According to the uncertainty transfer formula

37] , the uncertainty of heat flux and average heat transfer coeffi-

ient was estimated to be ±15 . 3% and ±15 . 87% at the low heat flux q = 20 W / c m 2 ). Similarly, the uncertainty of heat flux and average eat transfer coefficient was estimated to be ±5 . 75% and ±5 . 81% at he high heat flux ( q = 100 W / c m 2 ).

δQ

Q =

√ √ √ √ ( δ �m �

m

) 2 +

(δy 1 y 1

)2 (4)

δh

h =

√ (δQ

Q

)2 +

(δy 2 y 2

)2 (5)

y 1 = √

( δT in ) 2 + ( δT out ) 2 (6)

y 2 = √

8 ∑ i =5

(1

4 δT i

)2 +

(1

2 δT in

)2 +

(1

2 δT out

)2 (7)

1 = T out − T in (8)

2 = 1 4

8 ∑ T i −

1

2 ( T in + T out ) (9)

i =5


Fig. 4. (a) Curve of T with mass flow rate under different heat fluxes; (b) curve of h with mass flow rate under different heat fluxes.

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Fig. 5. Comparison with the previous published works.

Table 2

Geometric parameters of SJIMHS and OJIMHS [mm].

D in/out L L 1 L 2 W W 1 W 2 W 3 H H 1 D jet 2 42 2.85 5 22 3 2.5 0.5 5 1.5 0.5

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.7. Analysis and comparison of experiment results

As shown in Fig. 4 (a), the average temperature of the thermo-

ouples T 5 , T 6 , T 7 and T 8 varies with flow rate under different heat

ux, which approximately replaces the average temperature of the

eat transfer surface. It can be seen from the figure that when the

eat flux is constant, the temperature of the heat transfer surface

ecreases gradually with the increase of volume flow rate. In par-

icular, when the volume flow rate is 0.5 L/min and the heat flux is

00 W/cm ², the average temperature of the heat transfer surface is till lower than 60 °C, which is far lower than the critical tempera- ure of 85 °C for traditional electronics [38] . When the volume flow ate is small, changing the volume flow rate has a great impact

n the average temperature of the heat transfer surface, but with

he increase of volume flow rate, the effect of increasing volume

ow rate on the average temperature of the heat transfer surface is

maller. The reason for this phenomenon is when the volume flow

ate increases gradually, the convective heat transfer resistance de-

reases gradually until it is close to the thermal-conduction resis-

ance of the heat transfer rib plate. When the thermal-conduction

esistance dominates, the improvement of the heat transfer perfor-

ance by further increasing the flow will be smaller.

As shown in Fig. 4 (b), when the heat flux is constant, the aver-

ge convective heat transfer coefficient increases with the increase

f the volume flow rate, but when the volume flow rate is con-

tant, the change of heat flux has little effect on the heat trans-

er coefficient, which is consistent with study by Wu et al. [ 12 , 39 ]

hat minor changes in cooling medium parameters due to changes

f heat flow can be ignored. Therefore, the main factor affecting

he heat transfer coefficient of heat sink is the volume flow rate

nder the single-phase heat transfer state. The higher the volume

ow rate of the inlet, the faster the velocity of the cooling medium

jected from the jet hole, the thinner the boundary layer formed

hen scouring the heat transfer surface.

In addition, the experimental results in this paper are com-

ared with the results of the jet array cooling in published paper

27 , 28 , 39–44 ], as shown in Fig. 5 . The Reynolds number and the

verage Nusselt number of the heat transfer surface are defined as

ollows:

e = ρu D jet μ

(10)

u = h D jet λ

(11)

In the above formula, ρ , μ, λ are the density, dynamic viscosity oefficient and thermal conductivity of the fluid respectively, u is

he average velocity of the jet hole and D jet is the diameter of the

et hole. Observing Fig. 5 , it can be found that the jet-to-surface

5

pace ratio (Zn), the type of cooling medium and heat transfer

urface have a great influence on the heat transfer performance

f heat sink. When the jet-to-surface space ratio is the same, we

oticed that the average Nusselt number of heat sink with ribbed

late is better than that with smooth plate.

. Numerical model and calculation method

According to the experimental results, it is verified that the

JIMHS can achieve spectacular heat dissipation capacity with high

eat flux. In order to better understand the interaction mechanism

etween the flow and heat transfer of JIMHS, the overall numeri-

al simulation is adopted. In the numerical simulation, the effects

f heat flux, pressure drop and rib arrangement on the internal

ow and heat transfer of the heat sink were studied. In addition,

he working fluid and the heat sink material used in all the simu-

ations are the same with the experiment.

.1. Geometric model of SJIMHS and OJIMHS

Fig. 6 shows the three-dimensional structure of SJIMHS and

JIMHS, whilst Table 2 lists the main dimensions corresponding to

ach part. It should be noted that all the orifices have a diameter


Fig.6. Jet impingement/microchannel heat sink 3D model exploded view in (a) and 3D model diagram of each part in (b-1), (b-2) and (b-3).

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f 0.5 mm, which are arranged in a triangular staggered manner,

nd the jet to target space is 2 mm. For oblique-rib plate, the size

nd number of ribs are the same as that of straight-rib plate, it

nly has a different angle between ribs and horizontal direction of

7 °. In addition, considering the effect of the outlet reflux on the alculation results, the final fluid outlet length is extended to 6-8

imes the outlet diameter to eliminate the backflow phenomenon.

.2. Numerical calculation model and boundary conditions

According to literature investigation, the two-equation k − εurbulence model is widely used in the numerical simulation of

he jet impingement/microchannel heat sink and verified by ex-

eriment [ 17 , 31 ]. Considering the interaction between jets and the

isturbance of the fluid by the ribs, many vortex structures will

e formed in the heat sink. The RNG k-epsilon model, which is an

mprovement of the standard k-epsilon model, shows superior per-

ormance in predicting the flow features include strong streamline

urvature, vortices and rotation. Therefore, the RNG k − ε model ith moderate computational economy and acceptable accuracy is

nally selected for all the numerical simulations. In order to sim-

lify the calculation, the flow was assumed to be steady, incom-

ressible and continuous.

In this work, the commercial software Fluent 16.0 is used as

ow solver and the governing equations of incompressible flow in

he jet impingement/ microchannel heat sink are as follows:

Continuity equation:

∂ ( ρu i )

∂ x i = 0 (12)

Momentum conservation equation:

∂(ρu i u j )

∂ x j = − ∂ p

∂ x i + ∂

∂ x j

(μ

∂ u i ∂ x j

− ρu ′ i u ′

j

)(13)

Energy conservation equation:

∂ ( u i T )

∂ x j = ∂

∂ x j

(λ

ρc p

∂T

∂ x j

)(14)

Kinetic energy equation:

∂

∂ x i (ρk u j ) =

∂

∂ x j

[(η + ηt

σk

)∂k

∂ x j

]+ 2 ηt ∂ u i

∂ x j S i, j − ρε (15)

Dissipation rate equation:

∂

∂ x i (ρk u j ) =

∂

∂ x i

[(η + ηt

σε

)∂ε

∂ x i

]+ 2 C 1 ε ε

k ηt

∂ u i ∂ x j

S i, j − C 2 ε ρε 2

k

6

(16)

In the above formula, ρ is the liquid density, p is the pressure, i is the speeds in the x, y, and z directions, c p is the constant

ressure specific heat capacity, and ηt is the eddy viscosity coeffi- ient. S i, j , ηt and C 1 ε is given by the following equation, where C 2 ε s 1.68 and C μ is 0.085.

t = ρC μ k ε

(17)

i, j = 1

2

(∂ u i ∂ x j

+ ∂ u j ∂ x i

)(18)

1 ε = 1 . 42 − η(1 − η/ 4 . 38) 1 + 0 . 015 η3

(19)

As for the boundary conditions, the inlet boundary is set as

ressure inlet with a temperature of 283 K. The outlet is pressure

utlet, and the relative pressure is 0 Pa. The bottom heating sur-

ace is set to a constant heat flux, which increases from 40 W/cm ²o 100 W/cm ² with a step increment of 10 W/cm ². Only the heat ransfer is considered in the solid domain, the solid-liquid inter-

ace is set as no slip, and the rest of the walls are adiabatic.

The pressure-velocity coupling adopts SIMPLE method, and the

iscretization scheme is set as the standard for the pressure, QUICK

or energy, and second-order upwind for the remaining period.

hen the residuals of continuum equation and momentum equa-

ion reach 10 −5 , the convergence residuals of turbulence dissipa- ion term reach 10 −4 , and the convergence residuals of energy quation are less than 10 −7 , the convergence is considered as chieved.

.3. Mesh processing and verification of grid independence

The overall mesh of the heat sink is shown in Fig. 8 (a) and the

exahedral mesh of each part is generated by commercial software

CEM 16.0. Due to the complexity of the whole model, different

arts of the model are partitioned into blocks. Since the enhanced

all treatment function was used to calculate the near wall region,

he y + value is required to be around 1, and the maximum value annot exceed 5. To ensure that the y + value near the wall region s around 1 under the maximum flow condition, the grid height of

he first layer is set to 0.01mm, and the grid growth factor is set to

.3. Fig. 9 shows the grid of fluid region inside the heat sink with-

ut outlet extension. By slicing the grid longitudinally, the zoom-in

iews of grid in the near wall region and the jet hole region can

e obtained.


Fig. 7. Comparison of laterally-averaged wall temperature of the heat transfer surface for three different mesh densities along streamwise direction (a) SJIMHS, (b) OJIMHS.

Fig. 8. The overall mesh of the heat sink in (a) and precise regional mesh information of different part in (b) and (c).

Fig. 9. The zoom-in views of grid in the near wall region.

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In the process of grid independence verification, the number

f grids is changed by controlling the maximum grid size while

aintaining the same refined conditions of the near-wall region.

ig. 7 shows the comparison of laterally-averaged wall temperature

f the heat transfer surface for three different grid numbers of two

eat sink models. The change is observed to be less 1% by increas-

ng the grid number between the models for N 1 and N 2 . In addi-

ion, the Grid Convergence Index (GCI) method was used to test

he grid independence [45] . As shown in Table 3 , three successive

efined grids for each heat sink model were conducted to ensure

7

he accuracy of the numerical solutions. The refinement ratio be-

ween meshes N 2 and N 1 as well as between meshes N 3 and N 2 are

efined by r 21 and r 32 , respectively. The solution quantity of the av-

rage temperature of heat transfer surface are presented by φ1 , φ2 nd φ3 for each respective mesh. In addition, p is the observed rder of convergence between the studied meshes. According to

he calculation formula of GCI [46] , the Grid Convergence Index for

he N 2 mesh of each model ( GCI 21 fine ) were calculated. Based on the

esults of this Grid-independent test and weighing computational

osts, the grid of SJIMHS with 8,285,374 elements was adopted for


Table 3

Grid Convergence Index (GCI) verification.

φ = T [K], SJIMHS φ = T [K], OJIMHS N 1 , N 2 , N 3 20,106,763; 8,285,374; 4,565,147 29,536,274; 14,849,951; 6,675,643

r 21 1.34 1.26

r 32 1.22 1.31

φ1 308.98 303.98

φ2 309.94 304.93

φ3 310.91 306.41

p 1.67 1.18

GCI 21 fine 0.61% 1.26%

Fig. 10. (a) Comparison of simulated and experimental values of T and h under different heat flux;(b) comparison of simulated and experimental values of T and h under

different mass flow rate.

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ubsequent simulations. Similarly, the grid number of 14,849,951 is

elected to calculate OJIMHS.

.4. Comparisons between experimental results and simulation results

As shown in Fig. 10 (a), the average temperature and average

onvective heat transfer coefficient of the heat transfer surface cal-

ulated by simulation is compared with the experimental results

nder the same inlet mass flow rate. It can be seen that the vari-

tion trend of the simulation results is the same as that of the

xperimental results and there is little difference between them.

urthermore, the maximum relative error of the average tempera-

ure is only 0.33% and the maximum relative error of the average

onvective heat transfer coefficient is only 2.1%.

In order to further verify the reliability of the simulation results,

he experimental and simulated results at different mass flow rate

ere compared. The heat flux used in the cases of experiment and

imulation is 100 W / c m 2 . As shown in Fig. 10 (b), the curves of the

verage temperature and convective heat transfer coefficient of the

eat transfer surface measured in the experiment with different

ass flow rate are basically the same as that measured in the sim-

lation. Besides, the maximum relative error of the average heat

ransfer surface temperature between experiment and simulation

s about 1% and the maximum relative error of the average con-

ective heat transfer coefficient is about 9%, which are within the

rror tolerance. Therefore, it can be proved that the RNG k − ε tur- ulence model selected in the calculation has high accuracy in cal-

ulating the jet impingement/microchannel heat sink models and

he simulation results have high reliability.

. Analysis of numerical simulation results

.1. Comparison of temperature fields between SJIMHS and OJIMHS

As shown in Fig. 11 , the temperature distribution diagrams of

he heat transfer surface under different heat flux and the same in-

et pressure are obtained by numerical simulation. It is noticeable

hat under the same heat flux condition, the bottom heat trans-

er surface temperature of OJIMHS is generally lower than that of

8

JIMHS. The detailed temperature parameters of the heat transfer

urface of SJIMHS and OJIMHS are depicted in Table 4 . T max and

min represent the maximum and minimum temperature respec-

ively. T is the average temperature of the heat transfer surface

nd �T is the difference between the maximum and the mini-

um temperature. Observing Table 4 , it can be found that each

arameter of OJIMHS is lower than that of SJIMHS under the same

eat flux condition. In view of the difference of heat transfer per-

ormance, we speculated that the inclined arrangement of ribs will

ntensify the turbulence of the fluid, which is beneficial to inter-

upt the boundary layer and accelerate the mixing of cold and hot

uids, thus enhancing the convective heat transfer between the

ooling medium and the channel surface, and lowering the temper-

ture of the heat transfer surface. As shown in Fig. 12 , k is volume

eighted average of turbulent kinetic energy, which can reflect the

urbulence intensity of fluid. It can be found that the k of OJIMHS

s obvious higher than that of SJIMHS under all the calculated heat

ux when the inlet pressure is constant.

Moreover, as shown in Fig. 11 , the temperature is generally

ower near the upper of the picture, and higher near the bottom

f the picture, especially in SJIMHS. The upper part of the picture

s near the heat sink inlet and the lower part of the picture is

ear the heat sink outlet. The more details can be found in Fig. 13 ,

hich shows the local averaged heat transfer characteristics. T w,a v nd T f,a v are the laterally-averaged wall temperature of the heat

ransfer surface and laterally-averaged fluid temperature in the mi-

rochannel, respectively. As for the local area-averaged heat trans-

er coefficient, the formula for calculating it is defined as:

a v = q a v T w,a v − T f

(20)

here q a v is the averaged heat flux of the heat transfer surface

nd T f is the average temperature of the inlet and outlet of the

eat sink. The local average zone is in the middle of the rib and

he adjacent two rows of ribs, as shown in Fig. 13 . For the two heat

ink models, the fluid and heat transfer surface local area-averaged

emperature at the heat sink inlet are relatively low, and the con-

ective heat transfer coefficient reaches the maximum value. How-

ver, the heat transfer surface temperature and fluid temperature


Fig. 11. Comparison of temperature distribution diagrams at different heat flux.

Table 4

Numerical simulation result of properties of SJIMHS and OJIMHS.

Heat

flux/(W •cm −2 ) SJIMHS OJIMHS

T max / (K) T min / (K) T / (K) �T / (K) T max / (K) T min / (K) T / (K) �T / (K)

40 295.42 290.27 293.21 5.15 293.94 288.93 291.63 5.01

50 298.52 292.09 295.77 6.43 296.68 290.41 293.79 6.27

60 301.63 293.90 298.32 7.72 299.41 291.89 295.95 7.52

70 304.73 295.72 300.87 9.01 302.15 293.37 298.11 8.78

80 307.84 297.54 303.43 10.30 304.86 294.84 300.25 10.02

90 310.97 299.37 306.01 11.60 307.61 296.33 302.43 11.28

100 314.02 301.16 308.52 12.86 310.36 297.81 304.58 12.55

Fig. 12. (a) The curve of k under different heat fluxes; (b) the curve of k under different inlet pressure.

Fig. 13. Laterally-averaged wall temperature, fluid temperature and heat transfer coefficient of SJIMHS and OJIMHS along streamwise direction ( q = 100 W ·cm -2 , P in = 50 0 0 0 Pa).

9


Fig. 14. (a) T and h of the cooling surface under different heat fluxes( P in = 50 0 0 0 Pa ); (b) T and h of the cooling surface under different inlet pressure( q = 100 W · c m −2 ).

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radually increase along the flow direction and reach the maxi-

um value at the outlet. The main reason for this difference is

he “drift phenomenon” caused by horizontal crossflow, which can

e seen clearly in Fig. 16 . When the horizontal crossflow from up-

tream flows in the channel, the downstream vertical jet cannot di-

ectly wash down the cooling surface and drift toward the horizon-

al flow direction, which weakens the heat transfer performance

n the downstream jet area and increases the temperature of the

ooling surface [ 10 , 31 ]. However, the temperature of heat transfer

urface is decreasing at the edge of the surface, as shown in Fig. 11 ,

hich is agreed with the study by Wu et al. [39] that the influence

rom the adjacent wall enhance the heat transfer.

In comparison, it can be noticed that the temperature distri-

ution of the OJIMHS is much more uniform and there are fewer

verheated areas near the lower part of the picture. The reason

ould be inferred that the enhancement of turbulence is capable to

chieve more sufficient heat transfer between fluids in the whole

et passage, which makes the temperature distribution of fluids in-

ide the heat sink more uniform and forms a higher temperature

radient with the heat transfer surface [47] , then avoids the local

verheating phenomenon and reduces the adverse effect of hori-

ontal crossflow to some extent. As shown in Fig. 13 , it can be seen

learly that the local area-averaged fluid temperature of OJIMHS is

uch more uniform in the middle part of the heat sink. In addi-

ion, the local area-averaged heat transfer coefficient of OJIMHS is

ignificantly higher than that of SJIMHS at all measuring zones. In

onsequence, compared with the straight ribs, the oblique ribs can

ause better uniform flow field temperature to enhance heat trans-

er performance.

By analyzing the local heat transfer performance of the heat

ink in Fig. 13 , it is noticeable that the heat transfer performance

t the rib region is observably better than that at the rib free re-

ion for SJIMHS and OJIMHS. Especially for OJIMHS, the difference

s most obvious, which is reflected in the fluctuation of heat trans-

er surface temperature. It is speculated that two reasons are con-

ributed to this difference. Firstly, the existence of ribs increases

he heat transfer area, and the fluid will take away more heat

hen it passes through the rib region. Secondly, the ribs will break

he boundary layer and restrain the development of the bound-

ry layer, thus enhancing the heat transfer. Compared with straight

ibs, the direction of the fluid flow forms a certain inclination angle

ith the oblique ribs, so that the oblique ribs are more effectively

han straight ribs in inhibiting the development of the boundary

ayer. In the flow field analysis in Section 4.2 , the effect of rib ar-

angement on the flow field will be discussed in detail.

As shown in Fig. 14 (a), the average temperature of the heat

ransfer surface of OJIMHS is lower than that of SJIMHS under

even different heat fluxes, and the temperature difference be-

omes more and more obvious with the increase of heat flux.

n addition, with the increase of heat flux, the heat transfer sur-

t

10

ace average temperature of the two heat sinks increases gradually,

howing a linear change. As for the average convective heat trans-

er coefficient, the formula for calculating it is as follows:

= q A 1 A 2

(T w − T f

) (21) here, q is the heat flux of the bottom heating surface, A 1 is the

rea of the bottom heating surface( 40 × 20m m 2 ), and T w is the av- rage temperature of the heat transfer surface. As indicated in the

gure, the average convective heat transfer coefficient of OJIMHS is

bviously higher than that of SJIMHS under seven heat flux, with

n increase of about 20%. But the change of heat flux has little ef-

ect on the convective heat transfer coefficient for two models.

Fig. 14 (b) shows the average temperature and convective heat

ransfer coefficient of the heat transfer surface of OJIMHS and

JIMHS with the same heat flux as a function of inlet pressure.

bserving the figure, it is obvious that changing the inlet pressure

as a great influence on the average temperature and the average

onvective heat transfer coefficient. The higher the inlet pressure

s, and the higher the average convective heat transfer coefficient

s, the lower the average temperature is. In addition, under six dif-

erent inlet pressures, the average temperature of the heat trans-

er surface of OJIMHS is lower than that of SJIMHS, and the aver-

ge convective heat transfer coefficient of OJIMHS is higher than

hat of SJIMHS. Comparing the change of mass flow rate, we can

nd that when the inlet pressure is small, the inlet mass flow

ate of two heat sinks is not much different, basically the same.

owever, when the inlet pressure is larger, the mass flow rate dis-

arity between the two heat sinks gradually increases, and the

ass flow rate of SJIMHS is slightly higher than that of OJIMHS. It

ould be speculated that the oblique ribs exacerbate the fluid dis-

urbance, which causes an increase in the flow resistance. When

he inlet pressure is small, the velocity of the fluid is slow and

he disturbance caused by oblique ribs is relatively weak, so the

ow resistance caused by the disturbance is relatively small and

he inlet mass flow rate of the two heat sinks is not much dif-

erent. However, when the inlet pressure is large, the disturbance

aused by oblique ribs is intensified, so the flow resistance caused

y disturbance is relatively large and the mass flow rate of the

ooling medium flowing through OJIMHS is lowered. As shown in

ig. 12 (b), the difference of k between SJIMHS and OJIMHS is grad-

ally increasing with the increase of inlet pressure.

.2. Analysis of velocity field

In Section 4.1 , the temperature distribution of the two mod-

ls under different inlet pressures and heat fluxes is analyzed. In

iew of the heat transfer performance difference between the two

odels, we propose that the difference of temperature distribu-

ion is mainly caused by the fluid disturbance. In order to better


Fig. 15. Relative position of slices in JIMHS.

Fig. 16. The comparison of A-type velocity gradient diagram and streamline diagram between OJIMHS and SJIMHS: (a) q = 100 W ·cm -2 , P in = 50000 Pa, SJIMHS; (b) q = 100 W ·cm -2 , P in = 50 0 0 0 Pa, OJIMHS.

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nderstand the interaction mechanism between heat transfer per-

ormance and fluid disturbance, the velocity fields of two models

ere analyzed. Fig. 15 shows the relative position of the two slices

f SJIMHS and OJIMHS, wherein the lateral slice located in the XZ

lane is named slice A, and the longitudinal slice located in the ZY

lane is named slice B.

.2.1. Comparison of flow fields between SJIMHS and OJIMHS

Observing Fig. 16 , it can be seen for two models, the closer to

he inlet of the heat sink, the smaller the entrance velocity of the

et hole, the less obvious the “drift phenomenon” caused by hori-

ontal crossflow. This is consistent with the study by Huang et al.

31] that the jet velocity near the outlet is larger and the “drift

henomenon” is more obvious. The main reason for the velocity

ifference is the different length of the path from the jet hole to

he outlet of the heat sink. When the fluid enters the heat sink

rom the jet hole near the inlet, the length of the path from the jet

ole to the outlet is longer than that of the jet hole near the outlet,

o the pressure loss caused by the on-way resistance is larger. As

result, at the same inlet pressure, the greater the flow resistance

s, the smaller the jet velocity will be when it passes through the

et hole. This was verified by Cui et al. [10] in visual experiment.

11

n single-phase heat transfer regime, they found the crossflow ef-

ect was quite small in experiments due to the short path in cross-

ow direction. Consequently, they propose that measures should

e taken to diminish the adverse effect of crossflow when design-

ng the cooling applications for large areas.

It should be noticed from Fig. 16 that the fluid velocity near

he bottom heat transfer surface of OJIMHS is higher than that of

JIMHS, which is more evident near the outlet of the heat sink.

eanwhile, comparing the velocity gradient diagrams, it can be

ound that for OJIMHS, the fluid disturbance inside the heat sink is

tronger than that in SJIMHS, which is manifested that the change

n velocity gradient is more obvious, especially near the left and

iddle parts of the heat sink. Higher velocity means stronger tur-

ulence, which leads to higher convective heat transfer coefficient.

his explains why the heat transfer surface temperature distribu-

ion of OJIMHS is more uniform than that of SJIMHS, and there is

o local overheating area near the outlet of the heat sink.

Fig. 17 shows the B-type velocity gradient diagram and stream-

ine diagram comparison between OJIMHS and SJIMHS. It can be

een clearly that for SJIMHS, a pair of symmetrical vortex struc-

ures formed by the jet near the heat transfer surface directly be-

ow each jet hole. As for OJIMHS, the vortex structures formed un-


Fig. 17. The comparison of B-type velocity gradient diagram and streamline diagram between OJIMHS and SJIMHS: (a) q = 100 W ·cm -2 , P in = 50000 Pa, SJIMHS; (b) q = 100 W ·cm -2 , P in = 50 0 0 0 Pa, OJIMHS.

Fig. 18. Comparison of the isosurface vortex core region between OJIMHS and SJIMHS.

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er the jet hole are completely asymmetrical, and one of the vortex

tructures is obviously shifted toward the upper part of the chan-

el. Fig. 18 shows the distribution of isosurface vortex cores in the

ow field of the two heat sink models. It can be found that the

ortex structure in SJIMHS is more symmetrical, while the vortex

tructure in OJIMHS obviously deflects to one side, especially near

he outlet of heat sink. We speculated that the inclination of the

ibs makes the flow direction in the channel inclined to the main

ow direction. Under the joint action of the main stream and the

ow in the channel, the vortex structure formed by the jet deviates

o one side. The closer to the heat sink outlet, the more significant

he influence of horizontal crossflow. Therefore, the mutual influ-

nce between the main stream and flow in the channel is more

ntense.

In addition, due to the direction of the main flow forms a cer-

ain inclination angle with the ribs, the internal disturbance of

JIMHS is stronger and the interaction between the jet holes is

lso more significant. We can see clearly in Fig. 17 that the ve-

ocity in the gap between ribs and the upper cover of SJIMHS is

maller than that of OJIMHS, which verifies that the mutual influ-

nce between the adjacent jet holes of SJIMHS is inferior to that of

JIMHS.

Owing to the interaction between the jet holes, the mixing of

old and hot fluids is more sufficient, thus the temperature distri-

g

12

ution inside the heat sink is more uniform and a higher temper-

ture gradient with the heat transfer surface is formed, which will

nhance the heat transfer and avoid the occurrence of overheating

n the bottom heat transfer surface.

.2.2. Influence of pressure drop and heat flux

Since the change laws of changing inlet pressure and heat flux

n the flow field of two heat sinks are basically the same, only

he flow field of OJIMHS is selected for analysis. By analyzing the

verall change of Fig. 19 , it can be seen clearly that as the in-

et pressure increases, the velocity of the fluid increases and the

urbulence becomes more and more obvious, which is reflected in

he change of the velocity gradient level. In addition, as the in-

et pressure continues to increase, the velocity unevenness of the

et holes becomes more and more obvious. This is agree with the

tudy by Husain et al. [30] that the velocity distribution of jet holes

long the crossflow direction is uneven, especially at the large Re

umber. The main causes of this phenomenon are different path

engths and the increasing turbulence intensity as inlet pressure

ncreases, which were discussed in Section 4.2.1 .

As shown in the Fig. 20 , the A-type velocity gradient dia-

rams of OJIMHS are obtained by numerical simulation under the

ame inlet pressure and different heat flux. Observing the dia-

ram, changing heat flux has little effect on the internal flow of


Fig. 19. A-type velocity gradient diagrams of OJIMHS under different pressure drops: (a) q = 100 W ·cm -2 , P in = 10 0 0 0 Pa; (b) q = 10 0 W ·cm -2 , P in = 30 0 0 0 Pa; (c) q = 100 W ·cm -2 , P in = 50 0 0 0 Pa.

Fig. 20. A-type velocity gradient diagrams of OJIMHS under different heating heat flux: (a) q = 40 W ·cm -2 , P in = 50 0 0 0 Pa; (b) q = 100 W ·cm -2 , P in = 50 0 0 0 Pa.

t

t

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t

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c

d

5

w

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f

(

(

(

he heat sink. According to previous literature research, there were

hree states of flow in microchannel heat sink with the change of

eat flux, namely, single-phase flow, subcooled boiling and satu-

ated boiling. In the case of single-phase convection heat transfer

tate, the flow and heat transfer characteristics of the heat sink

re mainly related to the flow rate. The faster the flow is, the

tronger the disturbance is, the better the heat transfer perfor-

ance is [ 4 8 , 4 9 ]. Moreover, the flow rate of the internal fluid is

ainly related to the pressure drop between inlet and outlet.

For the case simulated in this work, when the heat flux is the

aximum, q = 100 W / c m 2 , the maximum temperature of the heat ransfer surface does not exceed 340K, which is in the single-phase

onvection heat transfer state. Therefore, the flow and heat transfer

haracteristics of the heat sink are mainly related to the pressure

rop.

. Conclusions

Two kinds of jet impingement/microchannel heat sink models

ere proposed in this work, which were studied by overall numer-

cal calculation and experiment. On the basis of the results, the

ollowing conclusions are drawn:

1) Under the same inlet pressure and heat flux, the cooling per-

formance of OJIMHS is better than that of SJIMHS, which is re-

13

flected in that the temperature distribution of OJIMHS is more

uniform and lower than that of SJIMHS. In addition, the average

convective heat transfer coefficient of the OJIMHS is obviously

higher than that of SJIMHS, with an increase of about 20%.

2) According to the analysis of temperature field and velocity field,

adding oblique ribs at the bottom heat transfer surface can

cause better fluid disturbance. The increase of turbulence is ca-

pable to interrupt the boundary layer development and acceler-

ate the mixing of cold and hot fluids, which makes the temper-

ature distribution inside the heat sink more uniform and forms

a higher temperature gradient with the heat transfer surface,

then enhance the heat transfer between the fluid and the wall,

avoid the local overheating phenomenon and reduce the ad-

verse effect of horizontal crossflow on the heat transfer perfor-

mance to some extent.

3) The experimental results are in good agreement with simula-

tion. Comparing the simulated and experimental vales of h and

T under different heat flux, the maximum relative error of T

between the simulated values and the experimental values is

only 0.33%, and the maximum relative error of h is only 2.1%.

In addition, when exploring the influence of mass flow rate

on heat transfer performance, the maximum relative error of

h between the simulated values and the experimental values is

9%, and the maximum relative error of T is 1%. When the vol-


Fig. 21. (a) T of the cooling surface under different heat fluxes( P in = 50 0 0 0 Pa ); (b) comparison of wetted areas of three heat transfer plates; (c) h of the cooling surface under different heat fluxes( P in = 50 0 0 0 Pa ).

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R

ume flow rate is 0.5 L/min and the heat flux is 100 W/cm ², theaverage temperature of the heat transfer surface is still lower

than 60 °C. Besides, the averaged heat transfer coefficient of 2.8 W / ( cm 2 · K) was achieved under the inlet fluid temperature of 283K and volume flow rate of 2.5 L/min in the experiment.

eclaration of Competing Interest

The authors declared that there is no conflict of interest. To the

est of our knowledge and belief, neither I nor any coauthors have

ny possible conflicts of interest.

RediT authorship contribution statement

H.C. Cui: Conceptualization, Methodology, Software, Validation,

ormal analysis, Investigation, Data curation, Writing - original

raft, Writing - review & editing. X.T. Lai: Methodology, Software,

ata curation. J.F. Wu: Software, Data curation. M.Z. Wang: Soft-

are, Data curation. W. Liu: Resources, Supervision, Project ad-

inistration, Funding acquisition. Z.C. Liu: Resources, Supervision,

roject administration, Funding acquisition.

cknowledgment

This work was supported by the National Natural Science Foun-

ation of China (grant no. 51736004 ).

ppendix

omparison of heat transfer performance between smooth plate and

ibbed plate

To show the effect of the increase of heat transfer area on the

eat transfer performance, we calculated the heat transfer perfor-

ance of heat sink with smooth plate under some conditions. The

asic size parameters of the heat sink with smooth plate is the

ame as SJIMHS and OJIMHS except that there is no rib array on

he heat transfer surface. The size parameters have been shown

n Fig. 6 and Table 2 . The same meshing strategy and turbulence

odel are used to perform numerical simulation on heat sink with

mooth plate. Fig. 21 (a) shows the average temperature of the heat

ransfer surface varies with heat flux on the bottom heating sur-

ace. It can be found that the average temperature of smooth plate

s significantly higher than that of SJIMHS and OJIMHS. When the

eat flux is 100 W · c m −2 , the average temperature of smooth plate s about 20 K higher than that of OJIMHS or SJIMHS, which shows

he heat transfer performance of heat sink can be significantly en-

anced by introducing ribs on the heat transfer surface. Fig. 21 (b)

hows the wetted area of three different types of heat transfer

ibbed plate. The wetted area of oblique-rib plate and straight-rib

late is the same, which is 1.875 times of smooth plate. Fig. 21 (c)

14

hows the average convective heat transfer coefficient of the heat

ransfer surface under different heat flux. It can be seen that the

verage convective heat transfer coefficient of OJIMHS is higher

han that of smooth plate, and that of smooth plate is slightly

igher than that of SJIMHS, which is similar with the study by Tra-

old et al [27] that in some cases, the Nusselt number of smooth

late is higher than that of ribbed rough plate. Through the previ-

us analysis, we have explained the reason why the average con-

ective heat transfer coefficient of OJIMHS is higher than that of

JIMHS. As for the situation that the average heat transfer coeffi-

ient of smooth plate is higher than that of straight-rib plate, we

nalyze the main reasons as follows. The introduction of ribs en-

ances the heat transfer performance by increasing the heat trans-

er area and enhancing the fluid disturbance. However, due to the

ame direction of rib arrangement and fluid flow in SJIMHS, the

ibs have little disturbance to the fluid and the improvement of

eat transfer performance of heat sink is mainly realized by in-

reasing the heat transfer area. On the other hand, the increase

f heat transfer area leads to an increase of flow resistance in the

hannel, and the flow velocity decreases with the same pressure

rop, resulting in the decrease of heat transfer coefficient.

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