Ashraf Zenkour - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah ۲۱۵۸۹, Saudi Arabia
Tariq Saeed - Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah ۲۱۵۸۹, Saudi Arabia
Khadijah Alnefaie - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah ۲۱۵۸۹, Saudi Arabia

This study focuses on the analysis of the bio-thermoelasticity response exhibited by biological tissues when their inner and outer surfaces are free from stress and exposing the outer surface of the skin to harmonic heating with heatlessness of the inner surface of the skin. The investigation employs a refined Green–Lindsay model for a comprehensive understanding of the phenomenon. A system of partial differential equations is written and the solution is obtained using the Laplace transform and numerical inverse Laplace. The current model's results for temperature, displacement, stress, and strain distributions are presented, and it is compared to various (coupled and uncoupled) models from previous literature. The relaxation times effect on the model with other models is clarified, the effect of time, and some vital parameters are also studied, and tabularly to illustrate the effect of blood perfusion on the four distributions.

Bio-thermoelasticity, classical coupled theory, Lord– Shulman theory, refined Green– Lindsay, Pennes' model, thermal wave theory, dual phase-lag theory, harmonic heating