Abstract
Purpose In the present paper, the new concept of "memory dependent derivative" in the Pennes' bioheat transfer and heat-induced mechanical response in human living tissue with variable thermal conductivity and rheological properties of the volume is considered. Design/methodology/approach A problem of cancerous layered with arbitrary thickness is considered and solved analytically by Kirchhoff and Laplace transformation. The analytical expressions for temperature, displacement and stress are obtained in the Laplace transform domain. The inversion technique for Laplace transforms is carried out using a numerical technique based on Fourier series expansions. Findings Comparisons are made with the results anticipated through the coupled and generalized theories. The influence of variable thermal, volume materials properties and time-delay parameters for all the regarded fields for different forms of kernel functions is examined. Originality/value The results indicate that the thermal conductivity and volume relaxation parameters and MDD parameter play a major role in all considered distributions. This dissertation is an attempt to provide a theoretical thermo-viscoelastic structure to help researchers understand the complex thermo-mechanical processes present in thermal therapies.