Theoretical analysis of thermal-viscoelastic behavior in living tissues using the two-phase-lag heat equation
摘要
The study of the thermomechanical behavior in applying heat to living tissues is of enormous relevance to improving clinical treatments in various patients. In this work, we study the viscoelastic theory coupled with a heat transfer phenomenon, resulting in a thermoviscoelastic study in a living tissue. We use a proposed Voigt thermoviscoelastic model and the heat transfer theory under the dual-phase-lag (DPL) model. The physical model focuses on the unidirectional study through the skin considered as a homogeneous medium. The governing equations are solved semi-analytically using the Laplace transform. The distribution of temperature and displacements, as well as the effect that the relaxation times of the thermoviscoelastic model and the DPL model have on them, are analyzed and graphically illustrated. Our results indicate that the DPL model exhibits a distribution in which displacements and the thermal front diffuse more slowly compared to the Pennes model and more smoothly than the Cattaneo–Vernotte model. Additionally, the viscoelastic effect on thermal stresses is more notable than what was previously reported in elastic analyses; however, it does not significantly impact the temperature distribution. Understanding these relationships can help design techniques that have less tissue damage. Our solution also allows us to recover other models, such as the elastic or even the Pennes model, for heat transfer in living tissue.