Abstarct: and specifying the adiabatic condition in the center of cylinder, the inverse analysis is performed for whole of the domain including the external laxyer. The solution at the external laxyer is In this paper, a compact finite difference is used to solve the two-dimensional transient heat transfer equation in a cylindrical domain of a functionally graded material. By considering the temperature –time histories in some internal laxyers pertaining to FG laxyers regarded as a boundary condition which can be imposed practically in heat treatment experiment. The numerical results obtained for the laxyers appeared between the FG laxyers have been compared with experimental results. The experimental results are obtained using the curve fitting approach from the time –history results of the FG laxyers. The absolute of the maximum difference between the numerical results and the experimental one at each time step within the whole domain is regarded as a global error. It is a function of time and proportional to it. The results for temperature time histories at computational nodes are compared with that of experiments obtained using the curve fitting techniques from the measured data. The overall behavior is close together. The differences are due to experimental errors, approximations encountered and numerical errors.