Steady and unsteady analytical solutions of three-dimensional heat transfer in a multi-layer and porous skin tissue

Although many models have been derived for heat transfer in the skin, analytical solutions for heat transfer provide more reliable results than numerical approaches. Due to the limitations of the in-vivo experiments, it is of great value to describe the thermal behavior of living tissues. In this paper, heat transfer in a multi-layer living tissue with different thermophysical properties in both steady and unsteady states are analyzed by using the Pennes’ and porous media models. Convective heat transfer in a three-layer skin is considered. It is found that both the results of the Pennes’ and porous models are almost identical. That is, by ignoring the blood perfusion term in the Pennes model, and instead, using the porous tissue properties similar results can be achieved, especially in the early stages of transient processes. It is also depicted that the magnitude of the blood temperature convection term is negligible compared to the temperature diffusion in the porous equation model. This indicates that the blood velocity within different layers of the skin can be ignored and only the thermophysical properties of the porous model can be considered in performing the analysis, which has less than a 3% difference compared to the Pennes model results.