The objective of this study is to predict numerically the optimal spacing between parallel heat generating boards. The isothermal boards are stacked in a fixed volume of electronic package enclosed by insulated lateral walls, and they are cooled by laminar forced convection of air with prescribed pressure drop. In the numerical procedure, governing equations for the solution of forced convection of constant property incompressible flow through one rectangular channel are solved. Resulting flow and temperature fields in each rectangular channel yield the optimal board-to-board spacing by which maximum heat dissipation rate from the package to the air is achieved. Next, generalized correlations for the determination of the maximum heat transfer rate from the package and optimal spacing between boards are derived in terms of prescribed pressure difference, board length, and density and kinematic viscosity of air. Finally, corresponding correlations are compared with the available two-dimensional studies in literature for infinite parallel plates.

References

References
1.
Bejan
,
A.
, and
Sciubba
,
E.
, 1992, “
The Optimal Spacing of Parallel Plates Cooled by Forced Convection
,”
Int. J. Heat Mass Transfer
,”
35
(
12
), pp.
3259
3264
.
2.
Bejan
,
A.
, 1984,
Convection Heat Transfer
,
2nd ed.
,
John Wiley & Sons
,
USA
, p.
157
.
3.
Bejan
,
A.
, 2000,
Shape and Structure From Engineering to Nature
,
Cambridge University Press
,
Cambridge
.
4.
Mereu
,
S.
,
Sciubba
,
E.
, and
Bejan
,
A.
, 1993, “
The Optimal Cooling of a Stack of Heat Generating Boards with Fixed Pressure Drop, Flow rate or Pumping Power
,”
Int. J. Heat Mass Transfer
,
36
(
15
), pp.
3677
3686
.
5.
Favre-Marinet
,
M.
,
Le Person
,
S.
, and
Bejan
,
A.
, 2004, “
Maximum Heat Transfer Rate Density in Two-Dimensional Minichannels and Microchannels
,”
Nanoscale Microscale Thermophys. Eng.
,
8
(
3
), pp.
225
237
.
6.
Campo
,
A.
, 1999, “
Bounds for the Optimal Conditions of Forced Convective Flows Inside Multiple Channels Whose Plates are Heated by a Uniform Flux
,”
Int. Commun. Heat Mass Transfer
,
26
(
1
), pp.
105
114
.
7.
Yüncü
,
H.
, and
Ekici
,
Ö.
, 2006, “
The Optimum Spacing Between Parallel Heat Generating Boards Cooled by Laminar Forced Convection
,”
J. Therm. Sci. Technol.
,
26
(
2
), pp.
1
10
.
8.
Morega
,
A. M.
, and
Bejan
,
A.
, 1994, “
Optimal Spacing of Parallel Boards with Discrete Heat Sources Cooled by Laminar Forced Convection
,”
Numer. Heat Transfer, Part A
,
25
(
4
), pp.
373
392
.
9.
Bejan
,
A.
, and
Fautrelle
,
Y.
, 2003, “
Constructal Multi-Scale Structure for Maximal Heat Transfer Density
,”
Acta Mech.
,
163
, pp.
39
49
.
10.
Bello-Ochende
,
T.
, and
Bejan
,
A.
, 2004, “
Maximal Heat Transfer Density: Plates With Multiple Lengths in Forced Convection
,”
Int. J. Therm. Sci.
,
43
(
12
), pp.
1181
1186
.
11.
Furukawa
,
T.
, and
Yang
,
W.
, 2003, “
Thermal Optimization of Channel Flows With Discrete Heating Sections
,”
J. Non-Equil. Thermodyn.
,
28
(
4
), pp.
299
310
.
12.
Bejan
,
A.
, 1982,
Entropy Generation Through Heat and Fluid Flow,
John Wiley & Sons
,
USA
.
13.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation
,
Taylor & Francis
,
New York
.
14.
Yilmaz
,
A.
,
Büyükalaca
,
O.
, and
Yilmaz
,
T.
, 2000, “
Optimum Shape and Dimensions of Ducts for Convective Heat Transfer in Laminar Flow at Constant Wall Temperature
,”
Int. J. Heat Mass Transfer
,
43
(
5
), pp.
767
775
.
15.
Tunc
,
G.
, and
Bayazitoglu
,
Y.
, 2002, “
Heat Transfer in Rectangular Microchannels
,”
Int. J. Heat Mass Transfer
,
45
(
4
), pp.
765
773
.
16.
Muzychka
,
Y. S.
, 2005, “
Constructal Design of Forced Convection Cooled Microchannel Heat Sinks and Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
48
(
15
), pp.
3119
3127
.
17.
Bar-Cohen
,
A.
,
Watwe
,
A. A.
, and
Prasher
,
R. S.
, 2003, “
Heat Transfer in Electronic Equipment
,”
Heat Transfer Handbook
,
Bejan
,
A.
, and
Kraus
,
A. D.
, eds.,
John Wiley & Sons
,
USA
, pp.
947
1027
.
18.
Kakaç
,
S.
,
Yüncü
,
H.
, and
Hijikata
,
K.
, eds., 1994,
Cooling of Electronic Systems
,
Kluwer Academic Publishers
,
Dordrecht, Netherlands
.
19.
Sathe
,
S.
, and
Sammakia
,
B.
, 1998, “
A Review of Recent Developments in Some Practical Aspects of Air-Cooled Electronic Packages
,”
ASME J. Heat Transfer
,
120
(
4
), pp.
830
839
.
20.
Kakaç
,
S.
, 2001, “
Introduction to ASI on Cooling of Electronics
,”
Cooling of Electronic Systems
,
Kakaç
,
S.
,
Yüncü
,
H.
, and
Hijikata
,
K.
, eds.,
(cited in) Ekici, Ö., The Optimum Spacing Between Parallel Heat Generating Boards Cooled by Forced Convection, Thesis for the Degree of Master of Science, Middle East Technical University
, p.
4
.
21.
Shah
,
R. K.
, and
London
,
A. L.
, 1978, “
Laminar Flow Forced Convection Heat Transfer and Flow Friction in Straight and Curved Ducts—A Summary of Analytical Solutions” (cited in
)
Laminar Flow Forced Convection in Ducts
,
Academic Press
,
New York
, p.
200
.
22.
Schmidt
,
F. W.
, 1978,
Personal Communication (cited in
)
Shah
,
R. K.
, and
London
,
A. L.
,
Laminar Flow Forced Convection in Ducts
,
Academic Press
,
New York
, p.
204
.
23.
Curr
,
R. M.
,
Sharma
,
D.
, and
Tatchell
,
D. G.
, 1987, “
Numerical Predictions of Some Three-Dimensional Boundary Layers in Ducts” (cited in
)
Shah
,
R. K.
, and
Bhatti
,
M. S.
, “
Laminar Convective Heat Transfer in Ducts
,” in
Handbook of Single-Phase Convective Heat Transfer
,
Kakaç
,
S.
,
Shah
,
R. K.
, and
Aung
,
W.
, eds,
John Wiley & Sons
,
New York
, Chap. 3.
24.
Bhattacharjee
,
S.
, and
Grosshandler
,
W. L.
, 1988, “
The Formation of Wall Jet Near a High Temperature Wall under Microgravity Environment
,”
ASME National Heat Transfer Conference
, Vol.
96
, pp.
711
716
.
25.
Petrescu
,
S.
, 1994, “
Comments on the Optimal Spacing of Parallel Plates Cooled by Forced Convection
,”
Int. J. Heat Mass Transfer
,
37
(
8
), p.
1283
.
You do not currently have access to this content.