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TECHNICAL PAPERS: Natural and Mixed Convection

# Compounded Heat Transfer Enhancement in Enclosure Natural Convection by Changing the Cold Wall Shape and the Gas Composition

[+] Author and Article Information
El Hassan Ridouane1

Department of Mechanical Engineering,  The University of Vermont, 201 Votey Bldg., 33 Colchester Ave., Burlington, VT 05405eridouan@cems.uvm.edu

Antonio Campo

Department of Mechanical Engineering,  The University of Vermont, 201 Votey Bldg., 33 Colchester Ave., Burlington, VT 05405

1

Corresponding author.

J. Heat Transfer 129(7), 827-834 (Jul 12, 2006) (8 pages) doi:10.1115/1.2712857 History: Received May 02, 2006; Revised July 12, 2006

## Abstract

This article addresses compound heat transfer enhancement for gaseous natural convection in closed enclosures; that is, the simultaneous use of two passive techniques to obtain heat transfer enhancement, which is greater than that produced by only one technique itself. The compounded heat transfer enhancement comes from two sources: (1) reshaping the bounded space and (2) the adequacy of the gas. The sizing of enclosures is of great interest in the miniaturization of electronic packaging that is severely constrained by space and∕or weight. The gases consist in a subset of binary gas mixtures formed with helium (He) as the primary gas. The secondary gases are nitrogen $(N2)$, oxygen $(O2)$, carbon dioxide $(CO2)$, methane $(CH4)$, and xenon (Xe). The steady-state flow is governed by a system of 2-D coupled mass, momentum, and energy conservation equations, in conjunction with the ideal gas equation of state. The set of partial differential equations is solved using the finite volume method, for a square and a right-angled isosceles triangular enclosure, accounting for the second-order accurate QUICK and SIMPLE schemes. The grid layouts rendered reliable velocities and temperatures for air and the five gas mixtures at high $Ra=106$, producing errors within 1% were 18,500 and 47,300 elements for the square and triangle enclosures, respectively. In terms of heat transfer enhancement, helium is better than air for the square and the isosceles triangle. It was found that the maximum heat transfer conditions are obtained filling the isosceles triangular enclosure with a He–Xe gas mixture. This gives a good trade-off between maximizing the heat transfer rate while reducing the enclosure space in half; the maximum enhancement of triangle∕square went up from 19% when filled with air into 46% when filled with He–Xe gas mixture at high $Ra=106$.

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## Figures

Figure 1

Sketch of the square and triangular enclosures

Figure 2

Comparison between the numerical and experimental mean Nusselt numbers within an isosceles triangular cavity filled with air for Case 1 (hot upper walls and cold base) and Case 2 (cold upper walls and hot base)

Figure 3

Influence of Rayleigh number Ra on the mean Nusselt number Nu for the square cavity and the isosceles triangular cavity when both are filled with air

Figure 8

Variation of the relative heat transfer coefficient hm∕B, across the square cavity, with molar gas composition of binary gas mixtures at Tref=300K and Ra=106

Figure 9

Variation of the relative heat transfer coefficient hm∕B across the triangular cavity with molar gas composition of binary gas mixtures at Tref=300K and Ra=106

Figure 10

Structure of the solution at Ra=106 and w=0.85 for air and the five binary gas mixtures trapped inside the triangular cavity: streamlines on the left and isotherms on the right

Figure 4

Evolution of the molecular viscosity with the molar gas composition of binary gas mixtures at Tref=300K

Figure 5

Evolution of the thermal conductivity with the molar gas composition of binary gas mixtures at Tref=300K

Figure 6

Evolution of the density with the molar gas composition of a binary gas mixtures at Tref=300K

Figure 7

Evolution of the heat capacity at constant pressure with the molar gas composition of binary gas mixtures at Tref=300K

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