Fractional triple-phase lag theory with non-singular kernels: analyzing the thermo-viscoelastic behavior of living skin tissue with bioheat transfer

Abstract

This study underscores the critical role of thermodynamics in understanding the response of living skin tissues to thermal interventions. Focusing on medical applications like laser therapy and cryotherapy, we introduce a novel fractional bioheat transfer model incorporating the triple-phase-lag (TPL) theory. This model, utilizing Atangana–Baleanu (AB) fractional derivatives with non-singular kernels, offers a more accurate representation of heat transfer and stress propagation within human skin compared to traditional models. Applied to viscoelastic skin tissue, our model reveals that increasing the fractional order leads to delayed thermal responses and gradual temperature and displacement variations, effectively capturing the memory effects inherent in viscoelastic materials. Notably, heightened viscosity significantly prolongs thermal recovery, increasing the time required for the tissue to return to its baseline state after thermal shock. These findings emphasize the crucial influence of viscoelastic properties and memory effects on the thermal and mechanical behavior of biological tissues. This research advances our understanding of thermal dynamics in human skin, demonstrating the value of combining fractional bioheat transfer models with TPL theory. This enhanced modeling framework has the potential to significantly improve therapeutic strategies in diverse medical applications.