The impact of fractional derivative on thermomechanical interactions in two-dimensional skin tissues throughout hyperthermia treatment

Abstract

This work aims to study the influence of fractional derivatives and thermal relaxation time on two-dimensional biological tissues using an eigenvalue-based approach. Understanding the heat transfer mechanism and its thermomechanical interactions with the skin tissue of patients is crucial for the successful implementation of thermal treatment procedure. The study employs Laplace and Fourier transforms, and the resulting formulations are applied to human tissues undergoing regional hyperthermia treatment for tumor therapy. The numerical inversion process for Laplace and Fourier transformations utilizes the Stehfest numerical inverse method. The results demonstrate that thermal relaxation time and fractional order parameter significantly influence all analyzed distributions. The numerical findings suggest that thermo-mechanical waves propagate through the skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

Keywords

• Analytical solutions
• Thermomechanical interaction
• Fractional time derivative
• Two-dimensional skin tissues
• Laplace- fourier transformations