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Research Papers: Electronic Cooling

# Numerical Simulation of Convective Heat Transfer Modes in a Rectangular Area With a Heat Source and Conducting Walls

[+] Author and Article Information
G. V. Kuznetsov

Faculty of Thermal Power Engineering, Tomsk Polytechnic University, 30 Lenin Avenue, 634050 Tomsk, Russia

M. A. Sheremet1

Faculty of Mechanics and Mathematics, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russiamichael-sher@yandex.ru

1

Corresponding author.

J. Heat Transfer 132(8), 081401 (May 20, 2010) (9 pages) doi:10.1115/1.4001303 History: Received November 05, 2008; Revised February 14, 2010; Published May 20, 2010; Online May 20, 2010

## Abstract

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.

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## Figures

Figure 1

A scheme of the system: (1–3) solid walls; (4) fluid; (5) heat source; (6) inlet; (7) outlet

Figure 2

Streamlines Ψ and temperature fields Θ at Re=700, Gr=106: (a) τ=20, (b) τ=40, and (c) τ=100

Figure 3

Variations in the average Nusselt number with the dimensionless time and the Grashof number at Re=700: (a) Nuright wall, (b) Nutop, and (c) Nubottom

Figure 4

Streamlines Ψ and temperature fields Θ at Re=500, τ=100: (a) Gr=104, (b) Gr=105, (c) Gr=106, and (d) Gr=107

Figure 5

Variations in the average Nusselt numbers with Grashof number for Re=500, τ=100: (1) Nuright wall, (2) Nutop, and (3) Nubottom

Figure 6

Streamlines Ψ at τ=100 depending on Re and Gr numbers

Figure 7

Temperature fields Θ at τ=100 depending on Re and Gr numbers

Figure 8

Variations of the average Nusselt number with Re and Gr at τ=100: (a) Nuright wall, (b) Nutop, and (c) Nubottom

Figure 9

The heat convection modes

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