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Transient Diffusion in Triangular Cylinders

Published online by Cambridge University Press:  09 September 2015

C. Y. Wang
C. Y. Wang*
Affiliation:
Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
*
*Corresponding author. Email: cywang@mth.msu.edu (C. Y. Wang)
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Abstract

A heated triangular cylinder is suddenly cooled in a constant temperature bath. The transient heat conduction problem is transformed to the Helmholtz equation related to the vibration of membranes. Using the membrane analogy, exact analytic solutions for the transient heat conduction problem for three triangular cross sections are found.

Keywords

80A20Diffusionheat conductiontransienttriangular
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 6 , December 2015 , pp. 818 - 826
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, 2nd Ed., Clarendon, Oxford, 1993.Google Scholar
[2]Wang, C. Y. and Wang, C. M., Structural Vibration-Exact Solutions for Strings, Membranes Beams and Plates, CRC Press, Boca Raton, Florida, 2014.Google Scholar
[3]Schelkunoff, S. A., Electromagnetic Waves, Van Nostrand, New York, 1943.Google Scholar
[4]Seth, B. R., Transverse vibrations of rectilinear plates, Proc. Indian Acad. Sci. A, 25 (1947), pp. 25–29.CrossRefGoogle Scholar