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)
Open Access
- 1 January 1967
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 24 (4), 315-322
- https://doi.org/10.1090/qam/211094
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.Keywords
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