Thermal memory and moving linear thermal shocks on heat transfer within biological tissues: an Atangana Baleneau fractional integral

Bioheat transfer is pivotal in a range of medical and daily applications, contributing to health and well-being. In hyperthermia treatment, it facilitates the elevation of temperatures in malignant tissues, thereby increasing their sensitivity to interventions such as radiation and chemotherapy, as well as in wearable monitoring devices, rehabilitation methods like heating pads and wraps, and electric blankets. This paper investigates the effects of thermal memory and dynamic linear thermal shocks on heat transfer within biological tissues. The research utilizes an advanced form of the Pennes equation for this analysis. The mathematical framework is based on an innovative time fractional generalized Fourier’s law, which can clarify particular aspects of atypical thermal diffusion phenomena. In the model being analyzed, the temperature gradient and its historical context influence the thermal flux. Additionally, at a specific location within the tissue, the thermal source induces a linear thermal shock at every instant. For both graphical and numerical simulations, Mathcad is employed to assess how the thermal memory parameter influences heat transfer.