Hyperbolic Heat Conduction in a Functionally Graded Hollow Sphere

Abstract

Non-Fourier hyperbolic heat conduction in a heterogeneous sphere is investigated in this article. Except for the thermal relaxation time, which is assumed to be constant, all other material properties vary continuously within the sphere in the radial direction following a power law. Boundary conditions of the sphere are assumed to be spherically symmetric, leading to a one-dimensional heat conduction problem. The problem is solved analytically in the Laplace domain, and the final results in the time domain are obtained using numerical inversion of the Laplace transform. The transient responses of temperature and heat flux are investigated for different non-homogeneity parameters and normalized thermal relaxation constants. The current results for the specific case of a homogeneous sphere are validated by results available in the literature.