ABSTRACT
In this chapter, the inverse determination of the thermal properties of simple metals which are temperature dependent is considered. In the particular case of simple metals, the nonlinear heat equation can be exactly linearised and the thermal properties and the temperature can be uniquely determined from a time-dependent temperature measurement function at a single sensor location within the conductor, provided that its continuous derivative never vanishes. The developed analytical method yields exact solutions, generally in implicit form, which can then be solved numerically. Solutions are obtained for infinite, semi-infinite and finite slabs with particular physical applications related to the cases of an instantaneous source, metals with a constant heat flux and the quencing of a flat plate in a tank filled with fluid. Some uniquenss results are revisited and analyzed for the more general case when the conductivity depends not only on the temperature but also on the space variable in a separable way.
