New analytic solutions of the one-dimensional heat equation for temperature and heat flow rate both prescribed at the same fixed boundary (with applications to the phase change problem)

Author:
David Langford

Journal:
Quart. Appl. Math. **24** (1967), 315-322

MSC:
Primary 35.78

DOI:
https://doi.org/10.1090/qam/211094

MathSciNet review:
211094

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Abstract: New solutions of the heat equation are exhibited for the case in which both the temperature and heat flow rate are prescribed at a single fixed boundary. The prescribed temperature and heat flow rate may be any arbitrary infinitely differentiable functions of time. The new solutions are applicable for one-dimensional (radial) heat flow in spheres, cylinders, and slabs.

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Additional Information

DOI:
https://doi.org/10.1090/qam/211094

Article copyright:
© Copyright 1967
American Mathematical Society