Generalized thermomechanical interaction in two-dimensional skin tissue using eigenvalues approach

The aim of this work is to analytically study the thermo-mechanical response of two-dimensional skin tissues when subjected to instantaneous heating. A complete understanding of the heat transfer process and the associated thermal and mechanical effects on the patient's skin tissues is critical to ensuring the effective applications of thermal therapy techniques and procedures. The surface boundary of the half-space undergoes a heat flux characterized by an exponentially decaying pulse, while maintaining a condition of zero traction. The utilization of Laplace and Fourier transformations is employed, and the resulting formulations are then applied to human tissues undergoing regional hyperthermia treatment for cancer therapy. To perform the inversion process for Laplace and Fourier transforms, a numerical programming method based on Stehfest numerical inverse method is employed. The findings demonstrate that blood perfusion rate and thermal relaxation time significantly influence all the analyzed distributions. Numerical findings suggest that thermo-mechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.