Abstract: The analytical formulae of the dimensionless unsteady temperature fields for an infinite plate, an infinite solid cylinder and a solid sphere made of functionally gradient materials (FGM) under convective boundary conditions are derived respectively by using the separation-of-variables method and the variable substitution method. The composition and the thermo-physical properties of the three kinds of FGM components with different shapes are of planar symmetric, axially symmetric and spherically symmetric distributions respectively. The influences of the FGM component shapes as well as the distributions of thermo-physical properties on their unsteady heat conductions are investigated via numerical calculations in contrast to homogeneous infinite plate, infinite solid cylinder and solid sphere respectively. The results reveal that the unsteady heat conductions for FGM components have a shape effect similar to that for homogeneous components, namely, the heat conduction rate is the fastest in sphere and is the lowest in plate; and that the heat conduction rate of FGM components can be improved by increasing both the thermal conductivity and the thermal diffusivity from the surface to the interior.

Key words: Functionally gradient materials, Shape effect, Unsteady heat conduction, Variable thermo-physical properties