An investigation of biological tissue responses to thermal shock within the framework of fractional heat transfer theory

Abstract

The present article addresses a novel mathematical model involving the Atangana-Baleanu (A-B) definition of fractional derivatives in time that offers a new interpretation of the thermo-mechanical effects inside skin tissue during thermal therapy. A Laplace transform mechanism is proposed to achieve closed-form solutions for prominent physical quantities, such as temperature, displacement, strain, and thermal stress. Computational results are obtained in time domains using an efficient numerical inversion algorithm of Laplace transform. The impact of the fractional parameter is investigated on the variations of the field quantities through the graphical results. The behavior of each physical field is speculated against the time parameter. The domain of influence of each field quantity is suppressed when the definition of the Atangana Baleanu fractional model is adopted, replicating that the waves under the A-B fractional model predict the finite nature of propagation compared to the conventional heat transport model. Further, we observe that the nature of the thermo-mechanical waves becomes stable earlier inside the tissue.