The determination of the thermal properties of a heat conductor in a nonlinear heat conduction problem

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 non-zero 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, semi-infinite and finite slabs.