We consider the two-dimensional problem of steady natural convection in a narrow Horizontal Cylindrical annulus filled with viscous fluid due to a sine temperature variation on the outer and adiabatic conditions at the inner boundaries. The solution is expanded in powers of a single combined similarity parameter introduced by [1], which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.
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ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems
July 17–22, 2005
San Francisco, California, USA
Conference Sponsors:
- Heat Transfer Division and Electronic and Photonic Packaging Division
ISBN:
0-7918-4731-4
PROCEEDINGS PAPER
Using Symbolic Calculation for Solving Natural Convection in a Narrow Horizontal Cylindrical Annulus Available to Purchase
Kamyar Mansour
Kamyar Mansour
Amirkabir University of Technology, Tehran, Iran
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Kamyar Mansour
Amirkabir University of Technology, Tehran, Iran
Paper No:
HT2005-72139, pp. 143-148; 6 pages
Published Online:
March 9, 2009
Citation
Mansour, K. "Using Symbolic Calculation for Solving Natural Convection in a Narrow Horizontal Cylindrical Annulus." Proceedings of the ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. Heat Transfer: Volume 1. San Francisco, California, USA. July 17–22, 2005. pp. 143-148. ASME. https://doi.org/10.1115/HT2005-72139
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