Exact Solution of the Multi-layer Skin Bioheat Equation in Cylindrical Coordinates for Thermotherapy with Different Varying Heat Fluxes

Abstract

Accurate prediction of temperature distribution during thermotherapy is a significant factor in the thermotherapy process. Thermotherapy equipment produces a different distribution spatial and time-dependent heat fluxes in the thermotherapy processes. This paper presents an exact analytical solution of steady and unsteady Pennes and porous bioheat equations in a cylindrical coordinate system for multi-layer skin with different spatial and time-dependent heat fluxes on the surface. The proposed analytical solutions are useful to make accurate temperature distribution in multi-layer skin tissue with various properties. The results show that the unsteady temperature distributions in both Pennes and porous models are the same in the initial times of process. When the temperature rises, the cooling effect of blood perfusion in the Pennes model increases the difference in temperature distribution for these two models. The skin surface temperature is linear versus time in constant and linear fluxes, and skin temperature increment has a second-degree trend versus time in the quadratic flux. The magnitude of the flux coefficient and the time of applying flux to the tissue are effective in increasing the temperature of the tissue and the skin surface. © 2021, Shiraz University.