Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Constant surface heating of a variable conductivity half-space

Author: Leonard Y. Cooper
Journal: Quart. Appl. Math. 27 (1969), 173-183
DOI: https://doi.org/10.1090/qam/99831
MathSciNet review: QAM99831
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Abstract: A solution to the problem of constant surface heating of an initially constant-temperature, $ T_0^*$, half-space where the material in question has a temperature-dependent thermal conductivity is obtained. The thermal conductivity, $ {k^*}$, is specifically given by $ {k^*} = k_0^*\exp \left[ {\lambda \left( {{T^*} - T_0^*} \right)/T_0^*} \right]$. The solution is valid for both heating and cooling of the material where $ \lambda $ and $ k_0^*$ are arbitrary in magnitude, and $ \lambda $ can be either positive or negative in sign.

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DOI: https://doi.org/10.1090/qam/99831
Article copyright: © Copyright 1969 American Mathematical Society

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