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
Full-text PDF Free Access

Abstract | References | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] D. Meksyn, New methods in laminar boundary layer theory, Pergamon Press, London, 1961
  • [2] J. Crank, Mathematics of diffusion, Oxford Press, London, 1956 MR 0082827
  • [3] J. B. Rosser, Transformations to speed the convergence of series, J. Res. Nat. Bureau of Standards 46, 56-64 (1951) MR 0040800
  • [4] H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids, Oxford Press, London, 1959 MR 0022294


Additional Information

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

American Mathematical Society