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 attains at the center of the bottom wall. The sidewalls are linearly heated, maintained at minimum temperature at top edges of the sidewalls and at temperature at the bottom edges of the sidewalls, i.e., . 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 and temperature difference aspect ratio for higher Raleigh number . 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 . The overall heat transfer process is shown to be tuned efficiently with suitable selection of .
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e-mail: m.sathiya@yahoo.com
e-mail: tanmay@iitm.ac.in
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December 2007
This article was originally published in
Journal of Heat Transfer
Technical Briefs
Effect of the Temperature Difference Aspect Ratio on Natural Convection in a Square Cavity for Nonuniform Thermal Boundary Conditions
M. Sathiyamoorthy,
M. Sathiyamoorthy
Department of Applied Mathematics,
e-mail: m.sathiya@yahoo.com
Birla Institute of Technology
, Mesra, Ranchi-835215, India
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Tanmay Basak,
Tanmay Basak
Department of Chemical Engineering,
e-mail: tanmay@iitm.ac.in
Indian Institute of Technology Madras
, Chennai-600036, India
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S. Roy,
S. Roy
Department of Mathematics,
e-mail: sjroy@iitm.ac.in
Indian Institute of Technology Madras
, Chennai-600036, India
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N. C. Mahanti
N. C. Mahanti
Department of Applied Mathematics,
Birla Institute of Technology
, Mesra, Ranchi-835215, India
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M. Sathiyamoorthy
Department of Applied Mathematics,
Birla Institute of Technology
, Mesra, Ranchi-835215, Indiae-mail: m.sathiya@yahoo.com
Tanmay Basak
Department of Chemical Engineering,
Indian Institute of Technology Madras
, Chennai-600036, Indiae-mail: tanmay@iitm.ac.in
S. Roy
Department of Mathematics,
Indian Institute of Technology Madras
, Chennai-600036, Indiae-mail: sjroy@iitm.ac.in
N. C. Mahanti
Department of Applied Mathematics,
Birla Institute of Technology
, Mesra, Ranchi-835215, IndiaJ. Heat Transfer. Dec 2007, 129(12): 1723-1728 (6 pages)
Published Online: March 12, 2007
Article history
Received:
July 24, 2006
Revised:
March 12, 2007
Citation
Sathiyamoorthy, M., Basak, T., Roy, S., and Mahanti, N. C. (March 12, 2007). "Effect of the Temperature Difference Aspect Ratio on Natural Convection in a Square Cavity for Nonuniform Thermal Boundary Conditions." ASME. J. Heat Transfer. December 2007; 129(12): 1723–1728. https://doi.org/10.1115/1.2768099
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