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TECHNICAL BRIEFS

# Natural Convection Patterns in Right-Angled Triangular Cavities with Heated Vertical Sides and Cooled Hypotenuses

[+] Author and Article Information
El Hassan Ridouane

Department of Mechanical Engineering,  The University of Vermont, Burlington, VT 05405

Antonio Campo

Department of Mechanical Engineering,  The University of Vermont, Burlington, VT 05405acampo@cem.uvm.edu

Jane Y. Chang

Department of Applied Statistics and Operation Research,  Bowling Green State University, Bowling Green, OH 43403

J. Heat Transfer 127(10), 1181-1186 (May 03, 2005) (6 pages) doi:10.1115/1.2033903 History: Received April 12, 2004; Revised May 03, 2005

## Abstract

The present investigation deals with the numerical computation of laminar natural convection in a gamma of right-angled triangular cavities filled with air. The vertical walls are heated and the inclined walls are cooled while the upper connecting walls are insulated from the ambient air. The defining apex angle $α$ is located at the lower vertex formed between the vertical and inclined walls. This unique kind of cavity may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method is used to perform the computational analysis encompassing a collection of apex angles $α$ compressed in the interval that extends from 5° to 63°. The height-based Rayleigh number, being unaffected by the apex angle $α$, ranges from a low $103$ to a high $106$. Numerical results are reported for the velocity field, the temperature field and the mean convective coefficient along the heated vertical wall. Overall, the matching between the numerically predicted temperatures and the experimental measurements of air at different elevations inside a slim cavity is of ordinary quality. For purposes of engineering design, a $Nu¯H$ correlation equation was constructed and also a figure-of-merit ratio between the $Nu¯H$ and the cross sectional area $A$ of the cavity was proposed.

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## Figures

Figure 1

Sketch of the upright right-angled triangular cavity

Figure 2

Plots of stream functions, isotherms and local Nusselt numbers Nuy for three apex angles α=63°, 45° and 15° sharing a small RaH=103

Figure 3

Plots of stream functions, isotherms and local Nusselt numbers Nuy for three different apex angles α=63°, 45° and 15° sharing a large RaH=106

Figure 4

Comparison between the numerical and experimental temperature profiles at three different elevations for a 15° triangular cavity

Figure 5

Comparison between the numerical and experimental dimensionless temperature profiles at three different elevations for a 10° triangular cavity

Figure 6

Variation of the mean Nusselt number Nu¯H with the Rayleigh number RaH parameterized by the apex angle α

Figure 7

Variation of the mean Nusselt number Nu¯H with the apex angle α parameterized by the Rayleigh number RaH

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