Laminar conjugate heat transfer in a rectangular area having finite thickness heat-conducting walls at local heating has been analyzed numerically. The heat source located on the left wall is kept at constant temperature during the whole process. Conjugate heat transfer is complicated by the forced flow. The governing unsteady, two-dimensional flow and energy equations for the gas cavity and unsteady heat conduction equation for solid walls, written in dimensionless form, have been solved using implicit finite-difference method. The solution has been obtained in terms of the stream function and the vorticity vector. The effects of the Grashof number Gr, the Reynolds number Re, and the dimensionless time on the flow structure and heat transfer characteristics have been investigated in detail. Results have been obtained for the following parameters: $103≤Gr≤107$, $100≤Re≤1000$, and $Pr=0.7$. Typical distributions of thermohydrodynamic parameters describing features of investigated process have been received. Interference of convective flows (forced, natural, and mixed modes) in the presence of conducting solid walls has been analyzed. The increase in Gr is determined to lead to both the intensification of the convective flow caused by the presence of the heat source and the blocking of the forced flow nearby the upper wall. The nonmonotomic variations in the average Nusselt number with Gr for solid-fluid interfaces have been obtained. The increase in Re is shown to lead to cooling of the gas cavity caused by the forced flow. Evolution of analyzed process at time variation has been displayed. The diagram of the heat convection modes depending on the Grashof and Reynolds numbers has been obtained. The analysis of heat convection modes in a typical subsystem of the electronic equipment is oriented not only toward applied development in microelectronics, but also it can be considered as test database at creation of numerical codes of convective heat transfer simulation in complicated energy systems. Comparison of the obtained results can be made by means of both streamlines and temperature fields at different values of the Grashof number and Reynolds number, and the average Nusselt numbers at solid-fluid interfaces.

1.
Dul’nev
,
G. N.
, and
Tarnovsky
,
N. N.
, 1971,
Heat Modes of Electronic Devices
,
Energy
,
.
2.
Jaluria
,
Y.
, 1998,
Design and Optimization of Thermal Systems
,
McGraw-Hill
,
New York
.
3.
Sathe
,
S.
, and
Sammakia
,
B.
, 1998, “
A Review of Recent Developments in Some Practical Aspects of Air-Cooled Electronic Packages
,”
ASME J. Heat Transfer
0022-1481,
120
, pp.
830
839
.
4.
Icoz
,
T.
, and
Jaluria
,
Y.
, 2004, “
Design of Cooling Systems for Electronic Equipment Using Both Experimental and Numerical Inputs
,”
ASME J. Electron. Packag.
1043-7398,
126
, pp.
465
471
.
5.
Icoz
,
T.
,
Verma
,
N.
, and
Jaluria
,
Y.
, 2006, “
Design of Air and Liquid Cooling Systems for Electronic Components Using Concurrent Simulation and Experiment
,”
ASME J. Electron. Packag.
1043-7398,
128
, pp.
466
478
.
6.
Hong
,
F. J.
,
Cheng
,
P.
,
Ge
,
H.
, and
Joo
,
G. T.
, 2007, “
Conjugate Heat Transfer in Fractal-Shaped Microchannel Network Heat Sink for Integrated Microelectronic Cooling Application
,”
Int. J. Heat Mass Transfer
0017-9310,
50
, pp.
4986
4998
.
7.
Polat
,
O.
, and
Bilgen
,
E.
, 2003, “
Conjugate Heat Transfer in Inclined Open Shallow Cavities
,”
Int. J. Heat Mass Transfer
0017-9310,
46
, pp.
1563
1573
.
8.
,
G.
, and
Narasimham
,
G. S. V. L.
, 2007, “
Laminar Conjugate Mixed Convection in a Vertical Channel With Heat Generating Components
,”
Int. J. Heat Mass Transfer
0017-9310,
50
, pp.
3561
3574
.
9.
Muftuoglu
,
A.
, and
Bilgen
,
E.
, 2008, “
Conjugate Heat Transfer in Open Cavities With a Discrete Heater at Its Optimized Position
,”
Int. J. Heat Mass Transfer
0017-9310,
51
, pp.
779
788
.
10.
Premachandran
,
B.
, and
Balaji
,
C.
, 2006, “
Conjugate Mixed Convection With Surface Radiation From a Horizontal Channel With Protruding Heat Sources
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
3568
3582
.
11.
Liaqat
,
A.
, and
Baytas
,
A. C.
, 2001, “
Numerical Comparison of Conjugate and Non-Conjugate Natural Convection for Internally Heated Semi-Circular Pools
,”
Int. J. Heat Fluid Flow
0142-727X,
22
, pp.
650
656
.
12.
Liaqat
,
A.
, and
Baytas
,
A. C.
, 2001, “
Conjugate Natural Convection in a Square Enclosure Containing Volumetric Sources
,”
Int. J. Heat Mass Transfer
0017-9310,
44
, pp.
3273
3280
.
13.
Jaluria
,
Y.
, 1980,
Natural Convection Heat and Mass Transfer
,
Pergamon
,
New York
.
14.
Bejan
,
A.
, 2004,
Convection Heat Transfer
,
Wiley
,
New York
.
15.
Kuznetsov
,
G. V.
, and
Sheremet
,
M. A.
, 2006, “
Two-Dimensional Problem of Natural Convection in a Rectangular Domain With Local Heating and Heat-Conducting Boundaries of Finite Thickness
,”
Fluid Dyn.
0015-4628,
41
, pp.
881
890
.
16.
Luikov
,
A. V.
, 1967,
Theory of Thermal Conductivity
,
Vysshaya shkola
,
Moscow, Russia
.
17.
,
V. M.
,
Polezhaev
,
V. I.
, and
Chudov
,
L. A.
, 1984,
Numerical Simulation of Heat and Mass Transfer Processes
,
Nauka
,
Moscow, Russia
.
18.
Samarsky
,
A. A.
, 1977,
The Theory of Difference Schemes
,
Nauka
,
Moscow, Russia
.
19.
Roache
,
P.
, 1976,
Computational Fluid Dynamics
,
Hermosa
,
Albuquerque, NM
.
20.
De Vahl Davis
,
G.
, 1983, “
Natural Convection of Air in a Square Cavity: A Bench Numerical Solution
,”
Int. J. Numer. Methods Fluids
0271-2091,
3
, pp.
249
264
.
21.
Dixit
,
H. N.
, and
Babu
,
V.
, 2006, “
Simulation of High Rayleigh Number Natural Convection in a Square Cavity Using the Lattice Boltzmann Method
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
727
739
.
22.
Kaminski
,
D. A.
, and
Prakash
,
C.
, 1986, “
Conjugate Natural Convection in a Square Enclosure Effect of Conduction on One of the Vertical Walls
,”
Int. J. Heat Mass Transfer
0017-9310,
29
, pp.
1979
1988
.