Thermal analysis of fractional hyperbolic two-temperature porous skin tissue subjected to fractional thermal diffusion by using diagonalization method

Abstract

This work is dealing with a model of a layer of porous skin tissue exposed to fractional thermal diffusion based on one relaxation time consideration. The surface plane of the skin tissue is influenced by variable thermal and chemical potential shocks with time. Laplace transform has been used, and the general solution was carried out analytically in the Laplace transform domain by applying the diagonalization method. The inverse of the Laplace transforms has been calculated by using a numerical method based on the Tzou formula. The dynamical and conductive temperature increments and the concentration have been computed and represented graphically with different cases. The two-temperature parameter, fractional order parameter, and porosity parameter have significant effects on the dynamical and conductive temperature increment and concentration of the diffusive material. Applying hyperbolic two-temperature of heat conduction on porous skin tissue based on fractio of heat conduction and thermal diffusion is a novel mathematical model. Moreover, this work introduces the diagonalization method as a different new method for this type of mathematical model.