Transient temperature fields in functionally graded materials with different shapes under convective boundary conditions

This paper presents analyses of the transient temperature fields in an infinite plate, an infinite solid cylinder and a solid sphere made of functionally graded materials (FGMs) under convective boundary conditions. The composition and the thermo-physical properties of the infinite FGM plate, the infinite FGM solid cylinder and the FGM solid sphere are of planar symmetric, axially symmetric and spherically symmetric distributions, respectively. The analytical formulae of the one-dimensional transient temperature fields for the three FGM solids are obtained respectively by using the separation-of-variables method and the variable substitution method. Numerical results reveal that the transient temperature fields of the FGM components exhibit similar shape effect to that of homogeneous components. The present work provides valuable basis for the investigation of the thermal shock resistance of FGMs with various shapes.