The determination of the thermal properties of a heat conductor in a nonlinear heat conduction problem
Abstract
This paper considers the inverse determination of the positive unknown thermal properties K(T), C(T) and the unknown temperature T(_{x, t}) in the nonlinear transient heat conduction equation. In addition to prescribed initial and/or boundary values, specified continuously differentiable temperature data T(x_{0}, t) with nonzero derivative at a single sensor location x = x_{0} is given. When K(T) and C(T) obey a certain relationship which enables one to linearise exactly the nonlinear heat equation then their dependence upon T is obtained explicitly, whilst the unknown temperature T(x, t) is obtained implicitly and is then calculated numerically. Results are presented and discussed for infinite, semiinfinite and finite slabs.
 Publication:

Zeitschrift Angewandte Mathematik und Physik
 Pub Date:
 2002
 DOI:
 10.1007/s000330028151x
 Bibcode:
 2002ZaMP...53..175L