Abstract
This paper presents a numerical analysis of the transient heat transfer problem arising when a functionally graded material is subjected to a fixed temperature difference. Varying the gradation of the system, the thermal performance of the material is assessed both in time-dependent and steady-state conditions by means of temperature profiles and entropy production. One of the main contributions of this paper is the analysis of the system in the transient, from which it is found that the entropy production has a non-monotonic behaviour since maximum and minimum values of this physical quantity could be identified by varying the grading profile of the material. The latter allows to propose an optimization criterion for functionally graded materials which consists of the identification of spatial regions where temperature gradients are large and find thermal conductivity profiles that attenuate those gradients, thus reducing the thermal stresses present inside the material.