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Proceedings of CHT-12. ICHMT International Symposium on Advances in Computational Heat Transfer.
July, 1-6, 2012, Bath, England

DOI: 10.1615/ICHMT.2012.CHT-12


ISBN: 978-1-56700-303-1

ISSN: 2578-5486

EXACT ANALYTICAL SOLUTIONS FOR VERIFICATION OF NUMERICAL CODES IN TRANSIENT HEAT CONDUCTION

pages 1755-1773
DOI: 10.1615/ICHMT.2012.CHT-12.1060
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SINOPSIS

This paper is intended to provide very accurate analytical solutions modeling transient heat conduction processes in 2D Cartesian finite bodies for small values of the time. Analysis of diffusion of thermal deviation effects indicates that, when the space and time coordinates satisfy a criterion developed in the paper, the simple transient 1D semi-infinite solutions may be "used" for generating extremely accurate values for temperature and heat flux at any point of a finite rectangle. Also, they may be "used" with excellent accuracy as short-time solutions when the time-partitioning method is applied (so avoiding the usually difficult integration of the short-convolution forms of Green's functions). A complex 2D semi-infinite problem is solved explicitly and evaluated numerically as part of the analysis. The proposed criterion is based on an accuracy of one part in 10n (n = 1,2,...,10,...), where n = 2 is for engineering insight and visual comparison while n = 10 is for verification purposes of large numerical codes.

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