This paper presents a cost effective semi-empirical analytical model for convective heat transfer in pin-fin heat sinks subjected to nonuniform heating set by a circular hot gas impinging jet. Based on empirical correlations taken from the open literature, temperature variations in the heat sink are obtained from the finite volume solution of the semi-empirical model. Based on a purpose-built experimental setup, measurements of a substrate temperature are performed using an infrared camera. These, along with the convective fluid temperature measured at the exit of the pin-fin array, are compared against analytical model predictions, with overall good agreement achieved. Subsequently, the influences of the convection Reynolds number, substrate thickness, and thermal conductivity of material on the distribution of substrate temperature are quantified by the validated model. It is demonstrated that the present model is capable of predicting local thermal behaviors such as the footprints of the pin fins. In addition, with the spreading resistance captured accurately, the model can be used for the design optimization of pin-fin/substrate systems subjected to nonuniform heating.

1.
Tahat
,
M.
,
Kodah
,
Z. H.
,
Jarrah
,
B. A.
, and
Probert
,
S. D.
, 2000, “
Heat Transfers From Pin-Fin Arrays Experiencing Forced Convection
,”
Appl. Energy
0306-2619,
67
, pp.
419
442
.
2.
Sara
,
O. N.
,
Yapici
,
S.
,
Yilmaz
,
M.
, and
Pekdemir
,
T.
, 2001, “
Second Law Analysis of Rectangular Channels With Square Pin-Fins
,”
Int. Commun. Heat Mass Transfer
0735-1933,
28
(
5
), pp.
617
630
.
3.
Sara
,
O. N.
, 2003, “
Performance Analysis of Rectangular Ducts With Staggered Square Pin Fins
,”
Energy Convers. Manage.
0196-8904,
44
, pp.
1787
1803
.
4.
Kim
,
D.
,
Kim
,
S. J.
, and
Ortega
,
A.
, 2004, “
Compact Modeling of Fluid Flow and Heat Transfer in Pin Fin Heat Sinks
,”
ASME J. Electron. Packag.
1043-7398,
126
, pp.
342
350
.
5.
Jeng
,
T. M.
, and
Tzeng
,
S. C.
, 2007, “
Pressure Drop and Heat Transfer of Square Pin-Fin Arrays in In-line and Staggered Arrangements
,”
Int. J. Heat Mass Transfer
0017-9310,
50
, pp.
2364
2375
.
6.
Saha
,
A. K.
, and
Acharya
,
S.
, 2003, “
Parametric Study of Unsteady Flow and Heat Transfer in a Pin-Fin Heat Exchanger
,”
Int. J. Heat Mass Transfer
0017-9310,
46
, pp.
3815
3830
.
7.
Naphon
,
P.
, and
Sookkasem
,
A.
, 2007, “
Investigation on Heat Transfer Characteristics of Tapered Cylinder Pin Fin Heat Sinks
,”
Energy Convers. Manage.
0196-8904,
48
, pp.
2671
2679
.
8.
VanFossen
,
G. J.
, 1982, “
Heat-Transfer Coefficients for Staggered Arrays of Short Pin Fins
,”
ASME J. Eng. Power
0022-0825,
104
, pp.
268
274
.
9.
Metzger
,
D. E.
,
Fan
,
C. S.
, and
Haley
,
S. W.
, 1984, “
Effects of Pin Shape and Array Orientation on Heat Transfer and Pressure Loss in Pin Fin Arrays
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
106
, pp.
252
257
.
10.
Chyu
,
M. K.
,
Hsing
,
Y. C.
,
Shih
,
T. I.-P.
, and
Natarajan
,
V.
, 1999, “
Heat Transfer Contributions of Pins and Endwall in Pin-Fin Arrays: Effects of Thermal Boundary Condition Modeling
,”
ASME J. Turbomach.
0889-504X,
121
, pp.
257
263
.
11.
Matsumoto
,
R.
,
Kikkawa
,
S.
, and
Senda
,
M.
, 1997, “
Effect of Pin Fin Arrangement on Endwall Heat Transfer
,”
JSME Int. J., Ser. B
1340-8054,
40
(
1
), pp.
142
151
.
12.
Moores
,
K. A.
,
Joshi
,
Y. K.
, and
Schiroky
,
G. H.
, 2001, “
Thermal Characterization of a Liquid Cooled AlSiC Base Plate With Integral Pin Fins
,”
IEEE Trans. Compon. Packag. Technol.
1521-3331,
24
(
2
), pp.
213
219
.
13.
Khorunzhii
,
I.
,
Gabor
,
H.
,
Job
,
R.
,
Fahrner
,
W. R.
, and
Baumann
,
H.
, 2003, “
Modelling of a Pin-Fin Heat Converter With Fluid Cooling for Power Semiconductor Modules
,”
Int. J. Energy Res.
0363-907X,
27
, pp.
1015
1026
.
14.
Fénot
,
M.
,
Vullierme
,
J. -J.
, and
Dorignac
,
E.
, 2005, “
A Heat Transfer Measurement of Jet Impingement With High Injection Temperature
,”
C. R. Mec.
1631-0721,
333
, pp.
778
782
.
15.
Goldstein
,
R. J.
,
Sobolik
,
K. A.
, and
Seol
,
W. S.
, 1990, “
Effect of Entrainment on the Heat Transfer to a Heated Circular Air Jet Impinging on a Flat Surface
,”
ASME J. Heat Transfer
0022-1481,
112
, pp.
608
611
.
16.
Coleman
,
H. W.
, and
Steele
,
W. G.
, 1999,
Experimentation and Uncertainty Analysis for Engineers
,
2nd ed.
,
Wiley
,
New York
.
17.
Baughn
,
J. W.
,
Hechanova
,
A. E.
, and
Yan
,
X. J.
, 1991, “
An Experimental Study of Entrainment Effect on the Heat Transfer From a Flat Surface to a Heated Circular Impinging Jet
,”
ASME J. Heat Transfer
0022-1481,
113
, pp.
1023
1025
.
18.
Goldstein
,
R. J.
, and
Franchett
,
M. E.
, 1988, “
Heat Transfer From a Flat Surface to an Oblique Impinging Jet
,”
ASME J. Heat Transfer
0022-1481,
110
, pp.
84
90
.
19.
Tao
,
W. Q.
, 2001,
Numerical Heat Transfer
,
2nd ed.
,
Xi’an Jiaotong University Press
,
Xi’an
, in Chinese.
20.
Metzger
,
D. E.
,
Berry
,
R. A.
, and
Bronson
,
J. P.
, 1981, “
Developing Heat Transfer in Rectangular Ducts With Arrays of Short Pin Fins
,” ASME Paper No. 81-WA/HT-6.
21.
Petukhov
,
B. S.
,
Genin
,
L. G.
, and
Kovalev
,
S. A.
, 1996,
Heat Transfer in Nuclear Power Equipment
,
Energoatomizdat
,
Moscow
, in Russian.
22.
Gnielinski
,
V.
, 1976, “
New Equations for Heat and Mass Transfer in Turbulent Pipe and Channel Flows
,”
Int. Chem. Eng.
0020-6318,
16
, pp.
359
368
.
23.
Lee
,
S.
,
Song
,
S.
,
Au
,
V.
, and
Moran
,
K. P.
, 1995, “
Constriction/Spreading Resistance Model for Electronics Packaging
,”
Proceedings of the Fourth ASME/JSME Thermal Engineering Joint Conference
, Vol.
4
, pp.
199
206
.
24.
Ma
,
H. B.
, and
Peterson
,
G. P.
, 2002, “
The Influence of the Thermal Conductivity on the Heat Transfer Performance in a Heat Sink
,”
ASME J. Electron. Packag.
1043-7398,
124
, pp.
164
169
.
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