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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)

1967
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Quarterly of Applied Mathematics
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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. Special solutions may be obtained by choosing special forms for the prescribed boundary temperature and boundary heat flow

doi:10.1090/qam/211094
fatcat:2z7dsulrvbc6znpizyxcsucrbi