Analytical solution of fractional order heat equation under the effects of variable thermal conductivity during photothermal excitation of spherical cavity of semiconductor medium

Abstract

In this investigation, the fractional model of heat equation in a semiconductor elastic medium with a spherical cavity is given. The model will be studied in one dimension with the influence of variable thermal conductivity which depends on the temperature. The medium has been investigated during the photothermal transport processes. The system of equations will explain the interference between the plasma–elastic–thermal waves. Laplace transform is applied to solve the governing equations. The complete solutions of main variables are obtained by using a numerical method based on Fourier series expansions. The thermal ramp type is applied on the inner surface of the cavity to obtain the physical quantities under investigation. The numerical computations of main physical quantities are illustrated and represented graphically. The time fractional order and the variable thermal conductivity have a great effect in main physical quantities.