Semi-analytical solutions for different non-linear models of dual phase lag equation in living tissues

Abstract

In this study, the heat transfer in a multilayer heated living tissue is investigated. A non-linear dual phase lag (DPL) heat conduction model is presented assuming temperature-dependent blood perfusion rate, heat conductivity and metabolic heat generation. Semi -analytical solutions for the non-linear model are obtained employing the Galerkin weighted residuals method. The effects of the variable thermophysical properties on the temperature distribution within the tissue are investigated through comparison of the results with the corresponding results for the constant thermophysical properties. The results show that the temperature dependence of the blood perfusion rate has a significant effect on the temperature distribution in the different layers of the tissue. As far as the tumor region is considered, 0.43 °C increase in its temperature is observed in comparison with that obtained assuming the constant blood perfusion rate at t = 1800 s. Moreover, increasing the temperature dependence of the thermal conductivity leads to the reduction in the temperature of the tissue except in the muscle layers. Considering the temperature-dependent metabolic heat generation increases the temperature of all of the layers compared to the corresponding temperatures obtained assuming the constant metabolic heat generation.