Bioheat Transfer with Thermal Memory and Moving Thermal Shocks

Abstract

This article investigates the effects of thermal memory and the moving line thermal shock on heat transfer in biological tissues by employing a generalized form of the Pennes equation. The mathematical model is built upon a novel time-fractional generalized Fourier’s law, wherein the thermal flux is influenced not only by the temperature gradient but also by its historical behavior. Fractionalization of the heat flow via a fractional integral operator leads to modeling of the finite speed of the heat wave. Moreover, the thermal source generates a linear thermal shock at every instant in a specified position of the tissue. The analytical solution in the Laplace domain for the temperature of the generalized model, respectively the analytical solution in the real domain for the ordinary model, are determined using the Laplace transform. The influence of the thermal memory parameter on the heat transfer is analyzed through numerical simulations and graphic representations.

Keywords

• bioheat transfer
• Pennes equation
• fractional calculus
• thermal shock