Estimation of thermal diffusivity profile in functionally gradient materials (Analytical consideration)

Temperature response in a functionally gradient material (FGM) which is subjected to transient heating is investigated in order to estimate the profile of the thermal diffusivity from the temperature response on the rear surface of the FGM. Focus is placed on a distribution parameter which yields the profiles of the thermophysical properties when there exists an exact analytical solution for the temperature response in the FGM. An explicit relationship is obtained between the distribution parameter and thermophysical properties on the rear surface. This explicit expression can represent the dependence of the temperature response on the thermophysical properties to ±4%. It is expected that this identification can provide useful insight into the estimation of thermophysical properties in FGMs. Usefulness of this relationship is also examined by comparing given and estimated profiles for the thermal diffusivity. Fair agreement is demonstrated, as far as the trend and the approximate magnitude are concerned.