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RESEARCH PAPERS

# Heightened Thermal Convection as a Result of Splitting a Square Cavity Diagonally in Half

[+] Author and Article Information
El Hassan Ridouane1

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

Antonio Campo

Department of Mechanical Engineering, The University of Vermont, 201 Votey, 33 Colchester Avenue, Burlington, Vermont 05405

1

Corresponding author.

J. Electron. Packag 128(3), 251-258 (Aug 09, 2005) (8 pages) doi:10.1115/1.2229224 History: Received May 04, 2005; Revised August 09, 2005

## Abstract

This investigation addresses the thermogeometric performance of a two-square cavity system contrasted against a two-isosceles triangular cavity system, with an exactly equal heating segment and comparable cooling segment. When one square cavity is cut diagonally in half, it results in a pair of isosceles triangular cavities. The isosceles triangular cavity on the left is heated from the left vertical wall, the top wall is insulated, and the inclined wall is cold; the so-called HIC triangular cavity. The isosceles triangular cavity on the right is heated from the right vertical wall, the bottom wall is insulated, and the inclined wall is cold; the so-called HCI triangular cavity. It may be speculated that the two-isosceles triangular cavity system may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method, accounting for temperature-dependent thermophysical properties of air, is employed to perform the computational analysis. Representative height-based Rayleigh numbers assume values up to $106$ to avoid oscillations that occur at a Rayleigh number between $RaH=2×106$ and $2.2×106$. Numerical results are reported for the velocity field, the temperature field, and the local and the mean convective coefficient along the heated vertical wall. Under a dominant conduction condition for $RaH=103$, the heat flux across the derived two-isosceles triangular system is 334% higher than its counterpart across the original two-square system. In contrast, for a dominant convection condition for $RaH=106$, this margin diminishes to 20%, but still constitutes a significant improvement. For the design of two-triangular cavity systems, a $NuH$ correlation equation has been constructed yielding a maximum error of 2% at $RaH=104$.

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## Figures

Figure 2

Comparison between the numerical and experimental mean Nusselt numbers for summer (Cases 1) and winter (Case 2) conditions

Figure 1

Sketch of: (a) A two-square cavity system, and (b) a derived two-isosceles triangular cavity system

Figure 3

Plots of stream functions and isotherms for the square and isosceles triangular cavities sharing a low RaH=103

Figure 4

Plots of stream functions and isotherms for the square and isosceles triangular cavities sharing a high RaH=106

Figure 5

Variation of the local Nusselt number Nuy along the hot vertical wall of the square and isosceles triangular cavities for: (a) A low RaH=103 and (b) a high RaH=106

Figure 6

Influence of Rayleigh number RaH on the mean Nusselt number NuH for the two-square cavity system and the two-isosceles triangular cavity system for 103⩽RaH⩽106

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