Transient Hyperbolic Heat Conduction in a Functionally Graded Hollow Cylinder

Hyperbolic heat conduction in a functionally graded hollow cylinder is investigated in this paper. Except for uniform thermal relaxation time, all other material properties of the cylinder are assumed to vary along the radial direction following a power-law form with arbitrary exponents known as the nonhomogeneity indices. When the cylinder is infinitely long, end effects can be ignored, and the one-dimensional heat conduction problem in the radial direction is solved analytically in the Laplace domain. The final transient solution of the problem in the time domain is obtained by numerical inversion of the Laplace transformed temperature and heat flux. The exact speed of the thermal wave in the nonhomogeneous cylinder is also obtained. Moreover, the effects of the nonhomogeneity indices and thermal relaxation time on the results are shown graphically by some illustrative examples. The current results are corroborated by the steady-state results for the homogeneous cylinder in the literature.