A Study of Turbulent Heat Transfer from Smooth and Rough Flat Plate SurfacesAll Theses and Dissertations
1969-5
A Study of Turbulent Heat Transfer from Smooth and Rough Flat Plate Surfaces Philip Tsungwen Lin Brigham Young University - Provo
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A STUDY OF TURBULENT HEAT TRANSFER FROM SMOOTH
AND ROUGH FLAT PLATE SURFACES
A Thesis
Master of Science
May, 1969
This thesis, by Philip Tsungwen Lin, is accepted in its present
form by the Department of Mechanical Engineering of Brigham Young Uni­
versity as satisfying the thesis requirement for the degree fo Master
of Science.
My beloved wife, Minghao
The author wishes to express his great appreciation to Dr.
Howard S. Heaton for his counsel and advice in the completion of this
thesis work. The suggestions of Professor Richard D. Ulrich are also
highly appreciated. Mr. John Kwan and Hill Hayes are appreciated for
their help in the design and construction of the experimental models.
I am also grateful to Mrs. Barbara Chen for her typing assistance.
Finally, I would like to express my deep love and appreciation
to my wife and son for their constant help and encouragement.
TABLE OF CONTENTS
LIST OF F I G U R E S ........................................ vii
LIST OF TABLES ........................................ ix
I. INTRODUCTION .................................. 1
Purpose and Scope of This Study Review of Previous Work Qualitative Description of Surface Rough­ ness Effect on Turbulent Heat Transfer
II. EXPERIMENTAL APPARATUS ........................ 5
Wind Tunnel and Calming Chamber Facility Experimental Model Aluminum Heater Plate Foam Insulating Plate and Wooden Frame
Power System Temperature Measuring System Velocity Measuring System
III. EXPERIMENTAL PROCEDURES ........................ 18
IV. EXPERIMENTAL R E S U L T S .......................... 21
Presentation and Discussion of Smooth Plate Data and Comparison with Theory Presentation and Discussion of Roughened Plate Data
V. CONCLUSIONS AND RECOMMENDATIONS .............. 40
Conclusions Recommendations
3. Experimental Models .................................. 9
5. Dimensions of Foam Insulating Plate.................. 13
6. Dimensions of Wooden Frame .......................... 14
7. Power S y s t e m ........................................ 16
8. Experimental Results for Plates Si, S2, S 3 ........... 22
9. Experimental Results for Plate SI with Nusselt Number Evaluated at Free Stream Temperature, by Reference Temperature Method and by Property Ratio Method ................ '24
10. Experimental Results for Plate N M 1 .................. 27
11. Experimental Results for Plate N M 2 .................. 28
12. Experimental Results for Plate N M 3 .................. 29
13. Experimental Results for Plate N M 4 .................. 30
14. Experimental Results for Plate M3 ................... 31
15. Data Correlated Curves for All Test P l a t e s ........... 32
16. Slope in Nusselt-Reynolds Number. Correlation vs. Roughness Height . . . . . .................... 34
17. Ratio of Roughness Nusselt Number to Smooth Nusselt Number vs. Reynolds Number with Relative Roughness as a Parameter................................ 35
vii
18. Nusselt Number vs. Relative Roughness Height with Reynolds Number as a Parameter ...................... 36
19. Stanton Number vs. Reynolds Number with Relative Roughness Height as a Parameter ...................... 37
20. Pitot Tube Locations.................................. 56
21. Airflow Velocity Profiles .............................. 57
22. Energy Balanced System for Variational Analysis of Temperature Distribution . .................... . 61
23. Thermocouple Calibration Curve ........................ 64
24. Manometer Calibration Curve ............................ 65
25. Analogy Circuit for the Measurement of Shape Factor of the Foam Insulating Plate.................. 67
26. Experimental Apparatus for the Measurement of the Thermal Conductivity of the Foam Insulating Plate................................................ 68
27. System for the Determination of the Thermal Conductivity of the Foam Insulating Plate ............ 69
28. Boundary Layer Development on a Piate with an Unheated Starting Length ............................ 72
29. Graphical Integration of j - L.j" | ^ j ^ Jy. . . . . 73
viii
2. Empirical Equations for Present Experimental Results . . 33
3. Experimental Results for Plate SI ..................... 44
4. Experimental Results for Plate S2 ..................... 45
5. Experimental Results for Plate S3 ..................... 46
6. Experimental Results for Plate NM1 .......... . . . . . 47
7. Experimental Results for Plate N M 2 ..................... 48
8. Experimental Results for Plate N M 3 ..................... 49
9. Experimental Results for Plate N M 4 ..................... 50
10. Experimental Results for Plate M3 ..................... 51
11. Temperature Variation Data ............................ 59
12. Tabulated Values off^^L_.|V-(—£— ................ 74 V •
ix
NOMENCLATURE
h
Kair
Kfoam
1
L
M
n
NM
Nu
Nuc
Nucp
Nur
Nur
plate length
slope in Nusselt-Reynold number(s) correlation
plate with a nonmetallic surface roughness
average Nusselt number based on plate length 1 and with properties evaluated at free stream temperature, hl/K .sir corrected Nusselt number
corrected Nusselt number using property ratio method
corrected Nusselt number using reference temperature method
average Nusselt number for the roughened plate
average Nusselt number for the smooth plate
total input electrical power
atmospheric pressure
pressure difference between the atmospheric pressure and the free stream static pressure
pressure difference between the stagnation pressure and the free stream static pressure
free stream static pressure
net electrical heating power
total input heating power
Reynold number based on plate length and with properties evaluated at free stream temperature
shape factor of the foam insulating plate
Stanton number
Experimental investigations of the surface roughness effect on
heat transfer have been extensively conducted since the initial work
by Cope; however, they were mostly limited to internal flow geometries--
circular tubes, annuli or rectangular ducts.
The purpose of this study was to investigate experimentally the
heat transfer for a turbulent incompressible fluid flowing over smooth
and artificially roughened plates with an unheated starting length,
with negligible pressure gradient and with Reynolds numbers ranging
from 2.5 x 10^ to 3 x 10"*. The plates were kept at constant temperature
for each run of the experiment and air was used as the test fluid.
The scope was limited to three aspects:
1. Smooth flat plates were studied to compare with existing
theoretical and experimental results and to provide basis
of comparison for the study of roughened plates.
2. Smooth flat plates with smooth and with roughened unheated
starting lengths were studied to see if there were any
different effects on heat transfer.
1
2
3. The effects on turbulent heat transfer of surface roughness
of different heights and of different material properties
uniformly spaced over flat plate were investigated.
Review of Previous Work
Since one of the first studies on heat transfer involving rough
surfaces was conducted by Cope (3) in 1941, a substantial amount of work
has been done concerning this aspect in the past 18 years. These works
involve different geometries and roughness configurations, but no method
for a general correlation relating the effect of surface roughness on
heat transfer coefficients has been developed so far. The purpose of
this section was not intended to review all these works but rather re­
stricted to summarize some of the major works, showing the development
of studies on the surface roughness effect on heat transfer problems.
Cope (3) studied the relationship between heat transfer coeffi­
cients and friction coefficients in rough circular pipes. Threads were
cut in the pipes to roughen the inner surfaces such that the pipe sur­
faces were actually covered with small pyramids. The experimental re­
sults showed that the heat transfer rate was increased initially
proportional to the roughness of the pipes but a considerable increase
in surface roughness improved the heat transfer rate very little.
Nunner (13) studied the roughness effect on heat transfer with
air flowing through a 5-cm diameter circular copper tube which was
artificially roughened with rings having equivalent sand roughness up
to 2.28 cm. The Reynolds numbers were sufficiently high so that the
completely rough hydraulic region was attained.
An extensive investigation on heat transfer and friction co­
efficients in smooth and sand grain roughened tubes was conducted by
3
Dipprey and Sabersky (4). Prandtl number effects were also observed
by adjusting the bulk temperature of distilled water flowing through
electrically heated tubes. The heat transfer similarity law similar
to Nikurad.se's (12) classical study on sand grain roughness presented
in Schlichting's work (16) was also developed and experimental results
were correlated and interpreted.
An analysis similar to Dipprey and Sabersky's work was also
developed by Owen and Thomson (14) and an experimental' investigation
of the heat-mass transfer analogy with a flat plate spanned in a low-
turbulence wind tunnel was conducted.
Sheriff and Gumley (17) experimentally studied heat transfer
and friction characteristics with air flowing through an annulus with
a discrete roughness surface. The roughness configuration was wire of
circular shape with a constant pitch-to-diameter ratio. They also
tabulated some of the significant works characterized by different
geometries and roughness configurations. These listed works included
those of Nunner, Dipprey and Sabersky, Edwards and Sheriff, Sams,
Walker and Rapier, Draycott and Lawther, Lancet, Fournel.
The effect of roughness (turbulence promoter) height and rough­
ness spacing was determined by Sutherland (18) in arrays of parallel
rods with discrete two-dimensional roughness elements in the form of
small fins transverse to the flow.
Gowen and Smith (5) also studied turbulent heat transfer from
smooth and rough surfaces and proposed, a semi-theoretical equation which
correlated their data adequately.
The works mentioned above were limited to internal flow geome­
tries except Owen and Thomson's flat plate experiment.
4
W. C. Reynolds (15) investigated experimentally the heat trans­
fer for turbulent flow over a flat plate and confirmed the analytical
result developed and described by Kays (7); however, Reynolds' work was
restricted to the problem of heat transfer for turbulent flow over a
"smooth" plate only.
Qualitative Description of Surface Roughness Effect on Turbulent Heat Transfer
Qualitative descriptions of surface roughness effects on the
transfer of heat have been discussed by Knudsen and Katz (9), Hinze (6),
Kays (7) and Schlichting (16) and can be summarized as follows:
Since the major resistance to heat transfer between a turbulent
fluid flow and a solid surface is believed to be confined to the very
thin laminar sublayer region immediately adjacent to the surface, the
protrusions of surface roughness which generate turbulent eddies and
disturb the laminar sublayer, decrease the laminar sublayer thickness
and hence augment the heat transfer.
For flow with a higher Reynolds number, a greater influence of
surface roughness on heat transfer may be expected since the effect of
increasing the Reynolds number is to decrease the thickness of laminar
sublayer and to increase the eddy diffusivity in the turbulent core.
The influence of Reynolds number on surface conditions and then on heat
transfer can also be observed from the Moody diagram for sand-roughened
plate presented by Schlichting (16). The diagram shows that a given
surface may be hydraulically smooth when Reynolds number is small and
become fully rough in the hydraulic sense as Reynolds number increases.
CHAPTER II
EXPERIMENTAL APPARATUS
The apparatus used in this experimental work included a wind
tunnel and calming chamber facility, experimental models, a power
system, a temperature measuring system, and a velocity measuring system
as shown in Figure 1.
Wind Tunnel and Calming Chamber Facility
The wind tunnel used for the experimental investigation was
located in the Mechanical Engineering Laboratory of Brigham Young
University.
The test section of the wind tunnel downstream of the nozzle
was 24 inches in length and 12 inches square in rectangular cross
section. The side panels of the test section were made of acrylic
plastic which provided a clear observation of the test model placed
inside the wind tunnel.
Air circulated in the laboratory was drawn through the wind
tunnel nozzle and test section by a ventilation fan powered by a
Westinghouse D. C. motor. The speed of the motor was controlled by
a variable resistance bank.
A calming chamber with filters normal to the flow direction
was placed in front of the wind tunnel to decrease the turbulence
level of the free stream entering the wind tunnel nozzle. The details
of construction of the calming chamber were described by Bingham (2).
5
6
The velocities obtainable with the calming chamber mounted on
the tunnel entrance ranged from about 28 fps to the maximum speed of
110 fps. A drape of flannel cloth could be placed over the front of
the calming chamber to obtain velocity as low as 10 fps.
Velocities inside the test section were measured transversely
in front of and above the test model. The results showed that reason­
ably uniform velocity profiles were obtained (see Appendix B).
The wind tunnel and calming chamber facility are shown sche­
matically in Figure 2.
The experimental model used in this study mainly consisted of
three parts: Aluminum heater plate, foam insulating plate and wooden
frame as shown in Figure 3 before being installed in the wind tunnel
test section.
roughened plates were constructed for this study. The active surfaces
of the smooth plates were sanded and polished to achieve hydraulically
smooth conditions. One plate with a metallic surface roughness was
obtained by machining the base aluminum material, while four plates with
nonmetallic surface roughness were obtained by placing polyethylene tape
strips (made from polyfilm. The Dow Chemical Company, Midland, Michigan)
on the aluminum surfaces as shown in Figure 3. The plate dimensions and
roughness material are shown in Table 1 with reference to Figure 4.
The bottom surface of each plate was uniformly coated with a thin
layer of electric heater cement ( product No. 6, Saurier-Eisen Technical
Fig. 2.--Wind tunnel and calming chamber facility
9
(b) back view of plate
(c) foam insulating plate
Fig. 4.— Locations of thermocouples and plate dimensions
TABLE 1
Plate £(inches) Surface Roughness
SI — —
The thermocouples were loca­ ted at locations 1, 2, 3, 4, and 5. Distributed rough unheated starting length was provided by the front part of the wooden frame and that of foam insulating plate.
S2 — —
Same as plate Si except that no thermocouple was placed at location 5 to measure the temperature between the heater and the center of the recessed portion of the foam insulating plate.
S3 — —
Same as plate SI except that the unheated starting length was artificially smoothed by placing polyethylene tape over it.
NM1 0.0076 polyethylene tape
NM2 0.0152 II Same as Plate Si
NM3 0.0228 II Same as Plate Si
NM4 0.0304 II Same as Plate Si
M3 0.0228 Machined aluminum
surface Same as Plate Si
Product Company), and cured in an electric furnace at 200°F for about
24 hours. This process provided the bottom surface of each plate with
good thermal conducting property and good electrical insulating prop­
erty. A volt-ohm milliammeter was then used to check if each cement
coating was free of electrical short circuits.
24-gauge nichrome electrical resistance heating wire of ap­
proximate 54 inches in length was attached with uniform spacing to the
cement coated surface of each plate by using glass cloth electrical
tape (Scotch brand, No. 27, 3M Company) as shown in Figure 3. The ni­
chrome wire served as the heat generator providing an approximately
uniform heating over the bottom of each plate.
On the center of each of the four sides of the plate, a hole
of 0.0315 inches diameter and 1.75 inches depth was drilled to provide
space for inserting the thermocouple used to measure the plate temp­
erature when the plate was heated.
Foam Insulating Plate and Wooden Frame
The foam insulating plate and wooden frame are shown in the
drawings of Figure 5 and Figure 6 respectively and together with
aluminum plate in an assembled form in Figure 3.
The foam insulating plate made from standard polyurethane
foam served two purposes. First, the center portion of the top sur­
face of the foam plate was recessed into a six inches square rec­
tangular shape with 0.25 inches depth for the positioning of the test
aluminum flat plate flush with the foam surface. Second, its low
thermal conductivity, K = 0.0112 BTU/hr.ft.F (measurement described in
Appendix D) made it a good thermal insulator, minimizing "back leak"
and "end leak" of heat from heater plate.
W///Z/////// 72Z?ZZ2iZk)
Fig. 6.--Dimensions of wooden frame
15
A wooden frame to support the foam plate was so constructed that
its side components could easily be fastened to the tunnel side panels
with metal screws. The leading edge of the wooden frame was constructed
in a shape of a half cylinder with 0.375 inches radius such that its
effect on the flow field was minimized.
The front part of the wooden frame together with that of the
foam plate constituted the unheated starting length in this study.
This length was 3.875 inches.
Power System
The power system is depicted schematically in Figure 7. The
nichrome electrical resistance wire, which was attached to the bottom
surface of the aluminum plate and connected through 2 electrical copper
wires to the power supply, acted as the heat generator. The input heat
power was supplied from a 110 volts, 60 cps, A.C. electrical power
source through a regulated D.C. power supply.
The electrical heat power was measured by using a D.C. wattmeter
(Westinghouse portable single phase wattmeter) checked against a volt­
meter (Westinghouse portable direct-current voltmeter) and a ammeter
(Westinghouse portable direct-current ammeter).
with a hand balanced thermocouple potentiometer (Leeds and Northrup
Company, Philadelphia).
A thermocouple junction box was used in the circuit to provide
quick measurement of the emf difference between any one of the thermo­
couples and the reference water-ice bath at 32°F.
Fig. 7.— Power system
Conversion Table for Thermocouple prepared by Leeds and Northrup Company.
The thermocouples were calibrated against an ESI 1302 thermometer as­
sembly as described in Appendix D.
Four thermocouples were inserted into the holes drilled on the
center of each side of the aluminum plate. Care was taken to assure
that each thermocouple junction was in good mechanical contact with the
plate surface inside the drilled holes. In most experiments, a thermo­
couple was also placed at the bottom of the plate heater to measure the
inside foam temperature which was used to calculate the heat loss
through the foam.
A thermocouple placed inside the calming chamber mounted in the
wind tunnel nozzle entrance was used to measure the free stream
temperature.
The data for free stream velocity and the velocity profiles
were measured by pitot tubes facing upstream and connected to an in­
clined manometer (The Meriam Instrument Company Model 40HE35).
The inclined manometer using Meriam red oil with specific
gravity equal to 0.827 was calibrated against a micromanometer (The
Meriam Instrument Company Model 34FB2) as described in Appendix D.
CHAPTER III
EXPERIMENTAL PROCEDURES
The experiment was conducted with the apparatus placed in the
positions as shown in Figure 1. The wind tunnel fan powered by the
D.C. motor was turned pn to circulate air through the calming chamber,
the wind tunnel nozzle and the test section. The airflow velocity was
adjusted as desired by ,a variable resistance bank. At the same time
the electrical heating power input to the test model was turned on.
About two hours was necessary for the test model to reach a
thermal steady state. The temperature of the aluminum heater plate
was measured with thepnocouples positoned in the drilled holes on the
sides of the plate pnd thermal steady state was assumed to be reached
when the output readings of the thermocouples through potentiometer
indicated approximately constant readings for a period of 20 minutes.
The temperature readings showed a difference of 2.0°F to 2.7°F between
the temperature indicated by the thermocouple inserted in the front
drilled hole and fhat indicated by the thermocouple inserted in the
rear drilled hole for pn average plate temperature of from 90°F to
160°F, while the temperature readings from the thermocouples inserted
in the side drilled h°?es showed an approximately the same value.
The steady state temperature of the plate, tp, was taken to be the
average value pf the four readings. The bottom plate temperature, t^,
was also measured with the thermocouple placed between the heater and
18
19
the center of the recessed portion of the foam plate. The bottom temp­
erature showed a difference of 1.2°F to -0.2°F from the averaged plate
temperature. The free stream temperature, t ^ , was measured with the
thermocouple positioned inside the calming chamber located at the wind
tunnel entrance. The temperature was checked against a thermometer
placed in front' of the calming chamber to insure that there were no
gross errors in the thermocouple measuring system. They showed devia­
tions from 0.1°F to 1.4°F; however, the reading from the thermocouple
positioned inside the calming chamber was taken to be the free stream
temperature in the data reduction. The variations of the various
temperature readings are discussed in Appendix C.
The pressure difference between atmosphere and free stream sta­
tic pressure, &Pa, and the pressure difference between the stagnation
and the static pressure, &PS, were read in inches of Meriam red oil
with sp.gr. = 0.827 by an inclined manometer through a pitot tube facing
upstream and located 2 \ inches above the rear part of the heated plate.
A mercury barometer was used to measure the ambient atmospheric pres­
sure. All these pressure data were used for the reduction of velocity
data.
The net electrical heating power, qnet, supplied to the alumi­
num heater plate was determined by subtracting the possible heat losses
from the total heat power measured with a wattmeter checked against a
voltmeter and an ammeter. The average of the two power readings was
taken to be the total heat power input. The significant heat losses,
after all the possible heat losses were considered, were the heat loss
through all sides of the foam, q^, and that through radiation from the
plate surface to the surroundings, qr.
20
The experiments were conducted mostly in the night time and at
a time when the environmental conditions were well controlled so that
the possible effect on the experimental investigation from the ma­
chinery operations and people working around was minimized.
With the measurements of the electrical heating power, average
plate temperature and free stream temperature available, the heat trans­
fer coefficients were determined according to Newton's law of cooling,
and the velocity data were calculated from pressure data according to
Bernoulli's equation.
The data was then correlated in terms of average Nusselt num­
ber Nu = hi , and Reynolds number Re = &.fUl , with roughness kair
height as parameter and are presented for analysis in the next chapter.
The details of the data reduction procedures are outlined in
Appendix A.
CHAPTER IV
EXPERIMENTAL RESULTS
Presentation and Discussion of Smooth Plate Data and Comparison with Theory
Three experimental investigations of turbulent fluid flowing
over three smooth plates of different conditions were conducted and
the resulting data are presented in Figure 8.
The three smooth plates were constructed as described in
Chapter II (Aluminum Heater Plate Section). However, the plate SI was
characterized by placing a thermocouple between the bottom of the plate
heater and the recessed portion of the foam to measure the temperature
used to calculate the heat loss through the foam. In the case of plate
S2, the averaged plate temperature was used instead to calculate the
heat loss through the foam. The plate S3 was characterized by having
the unheated starting length (front part of the wooden frame and that
of the foam plate) artificially smoothed by placing polyethylene tape
over it. No remarkable differences were observed from the results of
these three different test runs. The similarity of the results from
plate SI and S2 are obvious since the differences in the temperature
data of the averaged plate temperature and the heater's bottom temp­
erature are not significant. From the comparison of the data between
plates SI and S3, we conclude that the effect of the upstream dis­
tributed roughness on the unheated starting length provided by the
21
O
4
A°
O
/o2 __________________ |__j____________________________________ /0« z 3 -f 3 6 ? 6 5 loS I 3 - f
N5K>
23
front part of the wooden frame and that of the foam plate has negligible
effect on the downstream heat transfer from the heated plate section.
One question thus arises. What caused the transition to occur from
laminar to turbulent for the airflow over the plate with smoothed un­
heated starting length? The transition was probably caused by the
"step roughness" provided by the overlapped portion of the polyethylene
tape placed over the unheated starting length.
In Figure 9, the data from plate SI were again plotted with the
properties appearing in the nondimensional parameters (Re, Nu, Pr, etc.)
evaluated respectively at free stream temperature, at average temp­
erature of the free stream temperature and plate temperature (reference
temperature method) and at free stream temperature with property cor- t
rection factor (property ratio method) (7). The theoretical result
which was developed and described by Kays (7) and graphically integrated
to obtain the average Nusselt Number (see Appendix E) was also plotted.
The results show that the data reduced by using the reference temperature
method and the property ratio method can all be well correlated with a 0 8single curve (a straight line, Nuc = 0.0337Re , in log-log plot) and
thus indicate that these two methods are equally good. The data so re­
duced are about 5 to 1.5 percent higher than those evaluated at free 0.818
stream temperature (Nu = 0.0266 Re ) for the Reynolds number in the a ^range 6 x 10 to 3 x 10.
A comparison between the correlated empirical question,
Nu = 0.337Re^'^, and the theoretical equation, Nu = 0.0276Re v- c indicates that the result of the present experimental investigation de­
viates as much as +207o from that of the theoretical analysis. Careful
examinations of the experimental instrumentation and techniques were
Re Fig. 9.— Experimental results for plates SI with Nusselt number evaluated at free stream
temperature, by reference temperature method and by property ratio method.
ro-P*
25
conducted in an attempt to determine the possible causes to this 20%
deviation and indicate the dependability of present experiments (see
Experimental Uncertainty discussed in Appendix D). The care used in
the experimentation and the reproducibility of the present experimental
data resulting from the test runs of three smooth plates of different
conditions leads the author to believe that the present experimental
data are reliable.
Experimental evidences have indicated that, when a flat plate
of finite width is placed in a fluid stream flowing in the direction
of plate length, the boundary layer is no longer two-dimensional near
the side edges as it is along the centerline of the plate. Experi­
ments conducted by Elder and presented in Schlichting (16) indicated
that for stream flowing over a flat plate of finite span there arose
secondary flows near the side edges. The effect of secondary flows
remarkably increased the local friction coefficient along the edges.
From Reynolds analogy between momentum and heat transfer, we may
expect that this secondary flow effect may also cause an increase in
the local heat transfer coefficient. A series of experimental in­
vestigations on heat transfer for turbulent flow over flat plates of
various different widths conducted by Kwan (11) indicated that the
narrower the plate width the higher the average heat transfer coeffi­
cient. From the above-mentioned experimental results, this author
suspects that the deviation between the results of present experi­
ments and theoretical analysis could be partly caused by the edge
effect resulted from the finite dimensions of the heated test plates
since the theoretical result described in Kays was obtained by as­
suming turbulent flow over a "semi-infinite" plate. Also the
26
uncertainty in the effective starting point of turbulent boundary layer
may contribute part of the deviation. In addition, the nonuniformity
of plate temperature distribution as discussed in Appendix C could add
to the deviation.
In Figure 9, we also observe a relative increase in heat trans­
fer coefficient with lower Reynolds number. This probably results from
free convection which increases as Reynolds number decreases.
Presentation and Discussion of Roughened Plate Data
The results of the experimental investigation on heat transfer
for turbulent fluid flowing over roughened plates of different heights
and different roughness materials are separately presented by plotting
Nu vs. Re with relative roughness height, , as parameter in Figure 10
to Figure 14 to avoid the interference among the closely scattered data
points. The data-correlated curves for various roughened plates and
the smooth plate are plotted in Figure 15. All these curves which ap­
pear to be straight lines on log-log plot can be presented in empirical
equations of the form Nu = CRen which are tabulated in Table 2. The
change of slope, n, in the Nusselt number-Reynolds number correlation
for increasing roughness height is plotted in Figure 16. The data are
again presented in Figure 17 in the form of the ratio of Nusselt number
of various roughened plates to that of smooth plate vs. Reynolds number
with roughness height as parameter. In Figure 18, the data are plotted
in the form of Nusselt number vs. relative roughness height with Reynolds
number as parameter. In Figure 19, the data for the smooth plate and
for the nonmetallic roughness plates are plotted with Stanton number
vs. Reynolds number, having relative roughness height as a parameter.
Fig. 10.--Experimental results for plate NM1
roco
10’
fiu
Fig. 12.— Experimental results for plate NM3
r\
0
0
0
/o* [_ ------------------------------------ L----- ------L_— -------------------------------- ---------------------- ---------------- lo+ 2 4 6 8 /«5 Z ' j-
Re
AC
Nu
u>
Fig. 15.--Data correlated curves for all test plates
TABLE 2
Plate Nu = CRn Nur /Nus
Smooth 0.0266 Re0,818 1
NM4 0.0206 Re0,87 0.775 Re0 '052
RM3 0 950.0078 Re 0.0293 Re0 '132
Fig. 16.— Slope in Nusselt-Reynolds number correlation vs roughness height
Fig. 17.— Ratio of roughness Nusselt number to smooth Nusselt number vs Reynolds number with relative roughness as a parameter.
36
10'
Nu
t7
U
u
0
0
£ ( inch )
Fig. 18.--Nusselt number vs relative roughness height with Reynolds number as a parameter.
.Jt-IO3
Fig. 19.--Stanton number vs Reynolds number with relative roughness height as a parameter.
38
From Figure 15 and Figure 16, we observe that the larger rela­
tive roughness height starts having effect of increasing heat transfer
at lower Reynolds number while the smaller one does not and that the
larger relative roughness height has more effect on heat transfer co­
efficient at larger Reynolds number than the smaller one.
Qualatively, these phenomena can be explained as follows:
1. At the lower Reynolds numbers roughness of smaller
heights are submerged entirely within the laminar layer,
i.e., the roughness heights are in the hydraulically
smooth region and thus have no effect on heat transfer;
while the roughness of larger heights have already
penetrated through the laminar sublayer, i.e., the rough­
ness heights are in the roughness-transition region.
2. At larger Reynolds numbers, the thickness of the laminar
sublayer is thinned and the roughness of larger heights
penetrate further into the buffer layer and thus have
more effect on heat transfer coefficient than roughness
of smaller heights.
From Figure 18 we notice that for a given Reynolds number the
heat transfer coefficient increases as the height of roughness elements
increase. More increase in heat transfer coefficient for roughness of
larger height is also observed. It is also seen that the machined metal­
lic roughness does have more effect on increasing heat transfer coeffi­
cient than the nonmetallic roughness from the comparison of the data of
M3 and NM3. This is obviously due to the increase in conducting surface
area of the plate with highly conductive metallic roughness compared to
the plate with poorly conductive nonmetallic roughness.
39
From Figure 17, it is seen that the increase in heat transfer
coefficient due to roughness of as high as 50% were obtained.
Examing Figure 19, the plot of St vs. Re with relative rough­
ness height as parameter, we observe that the present results exhibit
behavior similar to those of Dipprey and Sabersky's (4).
CHAPTER V
From the results of this experimental investigation for turbu­
lent heat transfer from smooth and rough flat plate surfaces, we can
make the following conclusions and recommendations.
Conclusions
method are shown to be equally good for the correlation
of the current experimental data for smooth flat plates.
2. The distributed roughness provided by the unheated start­
ing length has a negligible effect on downstream heat
transfer over a smooth flat plate other than to insure
transition from laminar to turbulent flow.
3. The 20% deviation between the experimental and theoretical
results could be caused by the effect of the finite dimen­
sions of the plate, by the uncertainty in the effective
starting point of the turbulent boundary layer, by non-
uniform temperature distribution in the test plate and by
the instrumentation uncertainty.
4. For a given Reynolds number, roughness of larger height has
more effect on Nusselt number than roughness of smaller
height.
40
41
§ f The -roughness of machined surface has more effect on in­
creasing heat transfer than the parallel plastic trip wire.
This is pbviously due to the increase in conducting area
g f the metallic roughness.
^s high as 50% increases in heat transfer coefficients
^ere pbserved for roughened plates.
Recommendations
Since the theoretical result for turbulent heat transfer
frpm a smooth plate described by Kays has been well justi­
fied by experimental investigation, the 20% deviation
hefween the results of the present study and theoretical
analysis needs further investigation. The author suggests
that a smooth copper plate with a larger width than the
plate width of present study be constructed such that the
edge effect and nonuniform temperature effect on the re­
gulfs are eliminated.
I, fhe machining process for the construction of the metallic
ppughness should be improved such that an uniform roughness
height can be obtained.
The friction coefficients for the plates should be measured
go that more conclusions can be drawn from the heat transfer
data through the friction-heat transfer analogy.
If a method for the evaluation of the equivalent sand grain
fpughness can be developed, the information on friction co­
efficients presented by Schlichting may be used.
42
such that any unnecessary disturbance on the heat transfer
experiment can be minimized.
From the measurements described in Chapter 3, data were reduced
and presented in tabular form (Table 3 through Table 10).
Velocity Data Reduction Formula
The velocity data were reduced according to the Bernoulli's
equation and were presented in the form of Reynolds numbers. The pro­
cedures for the velocity data reduction were formulated as follows:
1. Read atmospheric pressure, P (inches of Hg) from mercurySL
barometer.
free stream static pressure,£>Pa (inches of Meriam red oil),
from the inclined manometer.
3. Determine the free stream static pressure according to the
equation:
through the voltage-temperature conversion table.
L (°R) = t^ (°F) +459.7
43
cp Or. o ]
^net BTU
F a sec hr hr hr hr.ft^.F
161.2 75.8 11.28 2.88 2.52 2.9 8.76 93.03 4.36 145 156 135.5
135.1 76.7 21 5.35 4.87 1.84 6 96.85 6.64 219 231 210
125.5 76.1 29.2 7.48 6.8 1.59 5.75 97.35 7.89 262 274 252
120.9 75.6 33.8 8.66 8.05 1.39 4.68 98.62 8.71 289.5 310 279.5
116 15 A 38.4 9.84 9.25 1.22 4.2 99.27 9.78 325 336 314.5
111.1 74.2 44.3 11.41 10.7 1.11 3.82 99.76 10.81 359.5 371 350
107.7 75 51 12.9 12.2 0.9 3.43 100.36 12.29 408 420 398
103.9 73.8 58.2 14.96 14.3 0.86 3.13 100.70 13.37 458 471 448
100.1 73.3 67.2 17.32 16.7 0.77 2.80 101.12 15.1 498.5 510 492.5
96.1 72.9 74.5 19.18 18.57 0.66 2.47 101.56 17.5 584 510 573
93.5 73.1 92.1 23.70 22.95 0.62 2.15 101.92 20 666 678 655
91.6 72.8 104.2 26.75 25.95 0.51 1.98 102.20 21.75 730 743 718
45
t p °F °F
BTU/hr BTU/hr ^net
46
tp to* u« S o -4 <*r ^net h Nu
128.9 79.8 28.2 7.1 1.48 5.11 94.435 7.7 253
123.6 79.4 33.3 8.36 1.29 4.61 95.125 8.62 284
112.7 78.8 48.6 12.3 1.05 3.54 96.57 11.4 376
107.1 76.9 56.2 14.2 0.815 3.15 97.095 12.87 425
99.4 76.4 78 19.7 0.62 2.4 98.14 17.05 565
95.2 75.3 95 24 0.556 2.08 98.524 19.8 657
92.9 74.9 107.4 27.3 0.535 1.875 98.75 21.95 730
47
fcp Re -4 xlO ^net h Nu
176.3 69.6 5.5 1.456 3.58 11.1 85.39 3.2 107.5
147.8 69.6 11.15 2.95 2.5 8.15 89.42 4.57 153.5
123.4 68.4 19.9 5.29 1.67 5.74 92.66 6.75 220.5
118.7 70.5 26.95 7.15 5.025 5.025 93.70 7.775 260
114.5 68.8 28 7.45 4.765 4.765 93.78 8.22 276
111.9 68.6 30.5 8.12 4.515 4.515 94.27 8.71 293
109.3 68.8 33.4 8.90 4.22 4.22 94.73 9.35 315
107.4 69 35.95 9.56 4.0 _ 4.0 95.05 9.93 333.5
102.9 68.6 42.25 11.2 3.58 3.58 95.53 11.12 374
99.4 6 / .5 45.85 12.2 3.32 3.32 95.89 12 404
96 68.2 54 14.25 2.9 2.9 96.42 13.85 466
91.2 69.4 68.4 18.05 2.275 2.275 97.20 17.85 600
86.3 67.7 95.3 25.2 1.94 1.94 97.55 21 707.5
103.6 77.4 58.2 14.6 2.74 2.74 99.71 15.2 503
102 77.6 . 64.2 16.1 2.55 2.55 99.93 16.4 556
99.5 76.8 75.6 19.0 2.37 2.37 100.16 17.65 586
98.1 77.9 83 20.85 2.11 2.11 100.49 19.9 658
95.6 78 101 25.4 1.84 1,84 100.84 22.9 758
48
tp uc~ Re / xlO"4 qr qnet h Nu
162.1 80.6 10.9 2.765 2.78 8.35 92.53 4.54 150
136.9 80.4 20.6 5.2 1.82 5.8 96.05 6.8 224
127.5 80.6 28.2 7.14 1.48 4.86 97.32 8.3 274
122.1 78.8 31.8 8.10 1.27 4.46 97.93 9.05 298.5
117.1 78.3 37.15 9.46 1.11 4.02 98.53 ' 11.05 365
111.8 77.5 43.75 11.15 1.03 3.56 99.07 11.55 382
108.5 78.4 48.9 12.46 0.79 3.12 99.95 13.25 437
105.1 78.2 56 14.3 0.73 2.82 100.11 14.9 491
101.4 77.8 64 16.3 0.71 2.47 100.48 17 563
96.6 77.5 79.2 20.2 0.64 2.04 100.98 21.1 700
93^2 77.9 97 24.6 0.6 1.65 101.41 26.5 875
92 76.8 106 26.9 0.41 1.62 101.63 26.8 890
49
tp Re /. xlO ^ qr '«k qUnet h Nu
122.6 83.1 29 7.29 1.22 4.11 97.06 9.84 322.5
113.9 83.4 38.2 9.60 0.92 3.89 97.6 12.81 420
99.5 74.4 50.2 13.05 0.75 2.61 99.03 15.8 525
97.7 74 52.5 13.62 0.726 2.47 99.4 16.77 557.5
95.85 73.7 55.7 14.35 0.642 2.3 99.4 17.98 598.5
94.1 73 60 15.62 0.6 2.2 99.6 18.9 629
91.7 71.7 67 17.45 0.514 2.08 99.8 19.95 667.5
88.8 71 73.9 19.26 0.45 1.85 100.1 22.5 753
88.5 71 78.1 20.4 0.45 1.82 100.1 22.9 765
85.5 70.3 98.6 25.8 0.45 1.58 100.4 26.4 884
84.7 69.2 108.2 28.23 0.32 1.59 100.5 26 880
160.2 79.1 12 3 2.74 8.5 93.65 4.62 152.5
152.4 79.6 14.2 3.56 2,4 7.15 95.34 5.24 173
133.7 80.1 21 5.26 1.67 5.69 97.53 7.28 250
118.8 79.2 32.8 8.215 1.19 4.15 99.65 10.06 331
110.7 79.6 43.9 11.0 0.91 3.25 100.74 12.95 427
104 79.8 56.6 13.92 0.7 2.53 101.66 16.8 554
97.1 79.7 85.7 21.42 0.64 1.82 102.42 23.5 775
94.7 79.2 99.3 24.78 0.42 1.62 102.82 26.6 878
TABLE 9
tp to. Rg / xl0 “4 qr qk qnet h Nu
157.8 77.2 11.7 2.94 2.68 8.23 97.62 4.85 161
147.2 75.9 14 3.52 2.3 7.32 98.91 5.5 185
120.1 75.6 25 6.28 1.33 4.6 102.60 9.22 306
116.7 75.9 28.4 7.13 1.22 4.26 103.05 10.1 335
112 75.7 32.7 8.21 1.05 3.76 103.72 11.42 379
108.1 75.9 37.4 9.4 0.93 3.34 104.26 13.04 433
104.2 75.4 43.7 11.0 0.83 2.99 104.71 14.5 481
100.9 75.7 48.1 12.1 0.71 2.63 105.19 16.68 553
98 76 56 14.05 0.62 2.3 105.61 19.2 636
95.5 75.6 65.3 16.4 0.56 2.12 105.85 21.2 704
93.4 75.8 74.5 18.7 0.49 1.88 106.16 24.1 800
90.9 75.2 38.2 22.15 0.43 1.69 106.41 27.1 900
89.6 73.4 99 9 24.82 0.44 1.79 106.30 26.3 876
51
fcp tco RexlO"^ qr ^net h Nu
154.5 77.3 12.8 3.25 2.63 8.22 88.27 4.574 151
142.4 75.6 15 3.81 2.13 7.7 89.29 5.35 177.5
122.6 76.3 22.3 5 .66 1.37 5.09 92.66 8.02 266
114 76.6 29.3 7.43 1.1 4.2 93.82 10 332
109.6 76.3 33.3 8.45 0.97 3.77 94.38 11.32 376
105.3 75.9 38.6 9.78 0.85 3.38 94.89 12.9 429
101.4 75.5 44.8 11.35 0.74 3 95.08 14.7 489
98.1 74.6 48.4 12.40 0.65 2.77 95.70 16.3 542
95.4 74.6 55.6 14.25 0.57 2.52 96.03 18.5 615
93 75.5 64 16.3 0.48 2.19 96.45 22.05 734
90.9 75,3 75 19.1 0.43 2 96.69 24.8 825
88.6 73.8 85.6 22.05 0.39 1.91 96.79 26.10 870
86.1 73.4 100.6 25.9 0.34 1.71 97.07 30.58 1020
5. Determine the airflow density according to the ideal gas law
u 1 b yyy ft3 ) = p__
RT
6 . Read the pressure difference between the stagnation pressure
and the static pressure, Pg (inches of Meriam red oil),
from the inclined manometer.
equation:
u*,( — )sec = /2gflPs (iI
. J 2^ p s (—
i 2 x 32.174 x 0.827 x 5.20 x (AP ) SL
= 16.63 — 9 co ( 5 )
8 . Calculate Reynolds number with aluminum plate length as the
characteristic length
Heat transfer coefficients were determined according to
Newton's law of cooling and were presented in the form of Nusselt number
The methods for data reduction were outlined as follows:
1. Find free stream temperature, t»<, (°F) averaged plate temp­
erature, t (°F), and plate bottom temperature, t^(°F), from
thermocouple readings.
T (°R) = t (°F) + 459.7p P
3. Measure total electrical power, P (watt) by averaging the
readings of the wattmeter and the voltmeter together with
the ammeter, and calculate the total input heating power
according to:
4. Calculate, the radiation heat loss according to:
qr (BTU/hr) = Ap Fp-sEp f (Tp - &
= (% X %) (1.0) (1.0) (0.1714 X 10'8) (t£ - i t )
f fTn (°R)= 0.004285 1 U2- -A
100 T„ (°R)
Fp_g = geometric configuration factor
<f - Stephan-Boltzmann constant
= 0.10416 (tb - O
where kfoam = 0.0112/BTU/hr.ft.F.
6 . Determine the net-input heating power
^net(BTU/hr) = 9t " “ 9k >
to Newton's law of cooling:
h (BTU/hr/ft?F.) = qnetM p (tp - t j
8. Calculate the average Nusselt number:
Nu I h kair
AIRFLOW VELOCITY PROFILES
The airflow behavior was studied in the wind tunnel test sec­
tion to determine the uniformity of the air flow in the neighborhood
of the experimental model. The velocity profiles were measured by
the system as described in Chapter 3. Pitot tubes located as shown
in Figure 20 were transversely moved to measure velocities at some
predetermined points. The results were presented in Figure 21 and
showed that reasonably uniform velocity profiles were obtained.
55
An analysis of the variations in the heated aluminum plate
temperature measured with temperature measuring instrumentations
placed at different locations was studied by taking the experimental
data of plate SI. The temperature data vs. velocity data for plate
SI were presented in Table 11 with reference to Figure 4 for the lo­
cations of the thermocouples.
The variations in temperature readings between the thermo­
couple located at the front and that located at the rear on the alumi­
num plate ranged from 2.0°F to 3.2°F. The two temperature readings
from the thermocouples inserted in the side of the aluminum plate were
observed to be about the same and were approximately equal to the
averaged temperature reading of the thermocouples located at the
front and rear drilled holes of the aluminum plate.
This analysis indicated that temperature distribution in the
aluminum plate was not quite in compliance with the requirement of con­
stant plate temperature assumption in present experiment. This might
result in +2% uncertainty in heat transfer coefficients.
Theoretical Analysis of Temperature Distribution
A theoretical method for predicting temperature distribution
in the aluminum plate was developed by employing the variational method
58
59
11.28 159.7
21 133.4
29.2 124.2
33.8 119.7
38.4 114.7
44.3 109.9
51 106.4
58.2 102.7
67.2 99.1
74.5 95
92.1 92.4
104.2 90.6
162.3 161.3
136.4 135.1
126.9 125.4
122.2 120.8
117.3 116
112.4 111.1
108.9 107.9
104.9 103.9
101.2 99.9
97.3 96.0
94.6 93.4
60
described in Arpaci's (1). A steady state energy balance was applied
to the plate system as shown in Figure 22 by assuming one-dimensional
(in the flow direction) heat conduction problem. The resulting dif­
ferential and variational formulations were:
d2t dx2
d2t dx2
By assuming 9(x) = t(x) - t
= tQ + aD x
h(x) = hD + (. Ibt-Z. A°.)x
<T I = (L d_e_ + ) + (_°L£)X (0o + a X2) + sd x2dx aJJ dx2 k<5 kcTA ° o ' k] c t^-t
k<T h + 3h
2 , ho + 5hn k <f c 30 -)
Thus the temperature distribution in the aluminum plate was:
ct(x) fco + tp" *~t> kf~
2 3 "
toe = free stream temperature
hQ = heat transfer coefficient in the neighborhood of plate front
h^ = heat transfer coefficient at the rear of plate
61
Fig. 22.--Energy balanced system for variational analysis of temperature distri­ bution.
62
£ = plate length
If the integral method is used, the resulting integral formula­
tion and temperature distribution are:
0 + a_ kd
t + ~~k7~ + 2 A ° 2 - -A1 f hQ + 5K^
<fk 12
Scientific Industries, Portland, Oregon) Model 1302 thermometer assem­
bly together with ESI Model 1303 thermometer adapter and ESI Model 300
potentiometric voltmeter bridge (PVB). Model 300 PVB gave direct
readings as the ratio between the resistance at the temperature to be
measured and the resistance at 0°C temperature. Temperature was then
determined from a conversion chart showing PVB reading vs. temperature
for the thermometer assembly. The resulting temperature correction
curve is presented in Figure 23.
The inclined manometer (Meriam Instrument Company Model
40HE35) used to measure velocity data was calibrated with a micro­
manometer (Meriam Instrument Company Model 34FB2) and the resulting
correction curve is shown in Figure 24.
The Westinghouse portable D-C voltmeter, ammeter and watt­
meter used to measure the electrical heating power were calibrated by
Electrical Engineering Laboratory and were found to have 0.5 per cent
accuracy for the voltmeter and ammeter and one per cent accuracy for
63
the wattmeter.
g0 loo izo '+° 160 l&0 100 zt0 t C f )
Fig. 23.— Thermocouple calibration curve
On
66
Measurements of Shape Factor and Thermal Conductivity for the Foam Insulating Plate
A technique similar to the electrical conducting sheet analogy
method described in the work of Kreith (10) was employed to determine
experimentally the geometric conduction shape factor for the foam in­
sulating plate, assuming two-dimensional steady state heat conduction.
The two-dimensional assumption was a good approximation to this three
dimensional problem because only the foam very near the edge of the
heated plate had a significant effect on the shape factor.
The analogy circuit is presented in Figure 25 and the shape
factor for the foam insulating plate so determined was 9.3.
The experimental apparatus for the measurement of the thermal
conductivity of the foam insulating plate was shown in Figure 26.
The apparatus was similar to the power system and temperature measur­
ing system employed in the wind tunnel heat transfer experiment except
that the test system in this case was an aluminum heater plate insulated
with foam of known shape in all sides as shown in Figure 27. The elec­
trical heating power was supplied to the test system and energy balance
was then applied to the system after it reached thermal steady state.
The thermal conductivity of the foam insulating plate was then determined
from measurements of the heating power, ambient temperature, the average
aluminum plate temperature and the shape factor of the foam. The shape
factor in this case was determined by a similar analogy technique also
shown in Figure and described in the determination of that of foam in­
sulating plate used in the heat transfer experiment.
The thermal conductivity of the foam insulating plate so deter­
mined with the method described as above was 0.0112 BTU/hr.ft.F
5___through the equation K = S ' AT
67
Fig. 25— Analogy circuit for the measurement of shape factor of the foam insulating plate
(a) volt-ohm milliammeter
(b) power supply
(c) electrical analogous system for the foam insulating plate
(d) electrical analogous system for the foam insulator used in the measure­ ment of Kfoam
68
Fig. 26--Experimental apparatus for the measurement of the thermal conductivity of the foam insulating plate
(a) test system
(f) reference bath
(g) power supply
Fig. 27.--System for the determination of the thermal conduc­ tivity of the foam insulating.
70
The experimental uncertainty in the calculated Nusselt number
and Reynolds number was estimated with the method described by Kline
and McClintock (8).
The probable uncertainties were 3.9 - 4.5%, for Reynolds
numbers, 4 - 4.4% for Nusselt numbers, and 5.7 - 6.3% for the ratio
of the Nusselt numbers of roughened plates to that of smooth plates.
APPENDIX E
Theoretical results for turbulent flow with constant free-
stream velocity flowing along a semi-infinite smooth plate as shown
in Figure 28 was described by Kays (7). Reynolds (15) further con­
firmed the theoretical result by his experimental investigation.
In order to constitute a basis for comparison with present
experimental work, this author determined the average Nusselt number
by graphically integrating the theoretical equation described in
Kays as follows:
local heat transfer coefficient was
hx = 0.0295 kairPr0.6 Re 0.8 X 0,8 xb - b )0'9J ^
and the average Nusselt number became
0.6Nu - <°-0295>’ Pr°'6 - <12> ±9 dx Re 0.8
if all length dimension were in inches. Taking Pr = 0.72 and
1 = 6 inches and integrating fL— — f 1 - — \1®*9 —r dx0.2 v x 'j y graphically as shown in Table 12 and Figure 29, we thus obtained
0.8
71
4.
Fig. 28.--Boundary layer development on a plate with an unheated starting length.
2 4 - 6 6 i o
Distance from the leading edge, x (in.)
Fig. 29.— Graphical Integration of
74
4 .5 0 ,93
75
we could easily integrate the equation and obtained
Nu = 0.30275 Re0,8
1. Arpaci, Vedat S. Conduction Heat Transfer. Reading, Mass,: Addison-Wesley Publishing ^ompany, 1966,
2. Bingham, Bruce D. "A Study of the Models of Transfer of Metabolic Heat from a Biological System to the Local Surroundings." Master Thesis, Brigham Young University, 1968.
3. Cope, W. F. "The Friction and Heat-Transmission Coefficients of Rough Pipes." Proc. Instn. Mech. Engrs., Vol. 145 (1941), pp. 99-105.
4. Dipprey, D. F., and Sabersky, R. H. "Heat and Momentum Transfer in Smooth and Rough Tubes at Various Prandtl Numbers." Int. J. Heat Mass Transfer, Vol, 6 (May, 1963), pp, 329-353,
5. Gowen, R, A,, and Smith, J. W. "Turbulent Heat Transfer from Smooth and Rough Surfaces." Int. J. Heat Mass Transfer, Vol. 11 (November, 1968), pp. 1657-1673.
6. Hinze, J. 0. Turbulence. New York: McGraw-Hill Book Company, 1959.
7. Kays, W. M. Convective Heat and Mass Transfer. New York: McGraw- Hill Book Company, 1966.
8. Kline, S. J., and McClintock, F. A. "Describing Uncertainties in Single-Sample Experiments." Mech. Engng. (January, 1953), pp. 3-8.
9. Knudsen, James G., and Katz, Donald L. Fluid Dynamics and Heat Transfer. New York: McGraw-Hill Book Company, 1958.
10. Kreith, Frank. Principles of Heat Transfer. Scranton: Interna­ tional Textbook Company, 1967.
11. Kwan, John C. W. "A Study of Turbulent Heat Transfer from Flat Plate with Transverse Temperature Variation." Master Thesis, Brigham Young University, 1969.
12. Nikuradse, J. "Laws for Flow in Rough Pipes." NACA TM 1292 (1950).
13. Nunner, W. "Heat Transfer and Pressure Drop in Rough Tubes." - A.E.R.E. Lib./Trans. 786(1958).
14. Owen, P. R., and Thomson, W. R. "Heat Transfer Across Rough Surfaces." J. Fluid Mech. Vol. 15 (1963), pp. 321-324.
76
77
15. Reynolds, W. C.; Kays, W. M.; and Kline, S. J. "Heat Transfer in the Turbulent Incompressible Boundary Layer." NASA Memo 12-1-58 W (December, 1958).
16. Schlichting, Hermann. Boundary Layer Theory. New York: McGraw- Hill Book Company, 1968.
17. Sheriff, N., and Gumley, P. "Heat Transfer and Friction Properties of Surfaces with Discrete Roughnesses." Int. J. Heat Mass Transfer, Vol. 9 (December, 1958), pp. 1297-1320.
18. Sutherland, W. A. "Improved Heat-Transfer Performance with Bound­ ary-Layer Turbulence Prometers." Int. J. Heat Mass Trans­ fer, Vol. 10 (May, 1959), pp. 1589-1599.
ABSTRACT
A study on turbulent heat transfer from smooth and rough flat
plate surfaces was conducted. Three smooth aluminum heater plates and
five artificially roughened plates were constructed. The exposed sur­
faces of the smooth plates were polished to achieve hydraulically smooth
conditions. One of the rough plates had matallic surface roughness
obtained by machining the base aluminum material,, while four plates had
roughness created by placing polyethylene tape strips on the aluminum
surfaces normal to the direction of flow.
The experiments were conducted in a wind tunnel with a Reynolds
numbers ranging from 2.5 x 10^ to 3 x 10"*. The results of heat transfer
investigation were presented in conventional plot of Nusselt number vs
Reynolds number with relative roughness height as a parameter. As high
as 507o increases in heat transfer coefficients were obtained for rough­
ened plates. The plates with metallic surface roughness showed larger
heat transfer coefficients than plates with the parallel plastic strips.
APPROVED:
1969-5
A Study of Turbulent Heat Transfer from Smooth and Rough Flat Plate Surfaces
Philip Tsungwen Lin
BYU ScholarsArchive Citation