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An Application of Conformal Mapping to a Three-Dimensional Unsteady Heat Conduction Problem

Published online by Cambridge University Press:  07 June 2016

Patricio A. Laura  and
M. Chi
Patricio A. Laura
Affiliation:
The Catholic University of America
M. Chi
Affiliation:
The Catholic University of America
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Summary

This paper deals with an unsteady-state three-dimensional heat conduction problem in a prismatic body which has a complicated boundary shape. Numerical techniques such as a relaxation method must be used to solve a problem of this type; this method, however, requires unusually large amounts of labour. The method used in this paper consists of the application of conformal mapping and numerical solution of a partial differential equation and is applied first to a prismatic body of square cross section for which the exact solution is well known. As a second application, the approximate solution for a problem involving a star-shaped cross section is presented.

Type
Research Article
Information
Aeronautical Quarterly , Volume 16 , Issue 3 , August 1965 , pp. 221 - 230
Copyright
Copyright © Royal Aeronautical Society. 1965

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References

1. Morse, P. and Feshbach, H. Methods of Theoretical Physics. McGraw-Hill, 1963.Google Scholar
2. Laura, P. A. On the Determination of the Natural Frequency of a Star Shaped Membrane. Journal of the Royal Aeronautical Society, p. 274, April 1964.CrossRefGoogle Scholar
3. Kantorovitch, L. V. and Krylov, V. I. Approximate Methods of Higher Analysis. Interscience Publishers, New York, 1958.Google Scholar