Heat Transfer Analysis of Memory-Dependent Derivative in Biological Tissue Subjected to a Moving Heat Source

Abstract

A new bioheat transfer equation is developed by introducing the memory-dependent derivative into dual-phase lag model. The heat transfer process of memory-dependent derivative in biological tissue under a moving heat source is studied. Besides, thermal conductivity is usually no longer constant at high temperature. The nonlinear temperature governing equation with considering variable thermal conductivity is formulated and the solutions are obtained by the methods of Kirchhoff and Laplace transformations. The influences of heat source velocity, variable thermal conductivity, relaxation time, and kernel function on the variation of temperature are analyzed.