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TECHNICAL BRIEFS

Effect of the Temperature Difference Aspect Ratio on Natural Convection in a Square Cavity for Nonuniform Thermal Boundary Conditions

[+] Author and Article Information
M. Sathiyamoorthy

Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi-835215, Indiam.sathiya@yahoo.com

Tanmay Basak

Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai-600036, Indiatanmay@iitm.ac.in

S. Roy1

Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036, Indiasjroy@iitm.ac.in

N. C. Mahanti

Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi-835215, India

1

Corresponding author.

J. Heat Transfer 129(12), 1723-1728 (Mar 12, 2007) (6 pages) doi:10.1115/1.2768099 History: Received July 24, 2006; Revised March 12, 2007

The present numerical investigation deals with steady natural convection flow in a closed square cavity when the bottom wall is sinusoidal heated and vertical walls are linearly heated, whereas the top wall is well insulated. In the nonuniformly heated bottom wall maximum temperature TH attains at the center of the bottom wall. The sidewalls are linearly heated, maintained at minimum temperature Tc at top edges of the sidewalls and at temperature Th at the bottom edges of the sidewalls, i.e., TcThTH. Nonlinear coupled PDEs governing the flow have been solved by the penalty finite element method with biquadratic rectangular elements. Numerical results are obtained for various values of Prandtl number (Pr)(0.01Pr10) and temperature difference aspect ratio A=[(ThTc)(THTc)](0A1) for higher Raleigh number Ra=105. Results are presented in the form of streamlines, isotherm contours, local Nusselt number, and the average Nusselt number as a function of temperature difference aspect ratio A. The overall heat transfer process is shown to be tuned efficiently with suitable selection of A.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the physical system

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Figure 2

Contour plots of Ra=105 for Pr=0.01 and A=0.1. Clockwise and anti-clockwise flows are shown via negative and positive signs of stream functions, respectively.

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Figure 3

Contour plots of Ra=105 for Pr=0.01 and A=0.7. Clockwise and anti-clockwise flows are shown via negative and positive signs of stream functions, respectively.

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Figure 4

Contour plots of Ra=105 for Pr=0.01 and A=0.9. Clockwise and anti-clockwise flows are shown via negative and positive signs of stream functions, respectively.

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Figure 5

Contour plots of Ra=105 for Pr=0.7 and A=0.1. Clockwise and anti-clockwise flows are shown via negative and positive signs of stream functions, respectively.

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Figure 6

Contour plots of Ra=105 for Pr=0.7 and A=0.9. Clockwise and anti-clockwise flows are shown via negative and positive signs of stream functions, respectively.

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Figure 7

Contour plots of Ra=105 for Pr=10 and A=0.9. Clockwise and anti-clockwise flows are shown via negative and positive signs of stream functions, respectively.

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Figure 8

Variation of local Nusselt number with distance at the bottom wall for Pr=0.7, (dashed line) and Pr=10, (solid line) at Ra=105

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Figure 9

Variation of local Nusselt number with distance at the sidewalls for Pr=0.7 (dashed line) and Pr=10 (solid line) at Ra=105

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Figure 10

Variation of average Nusselt number with temperature difference aspect ratio for Pr=0.7 (dashed line) and Pr=10 (solid line) at Ra=105

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