Fractional Order Dual-Phase-Lag Model of Heat Conduction in a Composite Spherical Medium

Abstract

In the paper, a solution of the fractional dual-phase-lag heat conduction problem is presented. The considerations are related to the heat conduction in a multi-layered spherical medium with azimuthal symmetry. The final form of the analytical solution is given in a form of the double series of spherical Bessel functions and Legendre functions. Numerical calculations concern the study of the effect of the order of the Caputo derivative on the temperature distribution in a composite solid sphere, hemisphere and spherical cone.