Study of generalized two-dimensional bioheat problem in the context of memory-dependent derivative

Understanding heat transfer and thermo-mechanical interactions in skin tissue is vital for effective thermal treatments. This study aims to analytically investigate the effect of Memory Dependent Derivative (MDD) on a two-dimensional Dual Phase Lag (DPL) bio-heat transfer model in skin tissue, utilizing the displacement potential approach. The surface boundary of the half-space experiences a thermal response under ramp-type heating conditions, with zero traction applied. To solve the governing equations, the study applies a combined Laplace-Fourier transform to obtain the field variables in the transformed domain. The Stehfest method and a seven-point Gaussian quadrature technique are employed for the simultaneous numerical inversion of these transforms. The results, presented graphically, illustrate the influence of ramp-type heating parameters (t₀), kernel functions (K(t-ζ)), and the time parameter (t) on the spatial variables x and y. The numerical results, along with the graphical representations, demonstrate that the memory effects significantly influence the distribution of the analyzed field variables.