Thermo-diffusive response of fractal spherical tumors under modified Green-Naghdi heat conduction models

Motivated by the widespread occurrence of fractal architectures in biological systems, the present study examines the thermodiffusive transport phenomenon in fractal spherical tumor cells. To adequately capture the underlying microstructural interactions, a nonlocal model of the Klein-Gordon type is formulated by incorporating a characteristic internal length scale together with an essential internal time-scale parameter. The coupled bioheat-diffusion law is developed through an analogy with viscoelastic theory, thereby embedding memory-dependent effects within a finite slipping interval. The spherical tumor is assumed to be mechanically traction-free on both its inner and outer boundaries, while the interior and exterior surfaces are simultaneously subjected to transient thermal and biochemical excitations. The governing equations are solved by employing the Laplace integral transform, and the resulting transformed solutions are numerically inverted using Zakian's method. The computational analysis demonstrates that thermodiffusion, internal length and time scales, and the variation of fractal dimensions exert a pronounced influence on the thermal and diffusive behavior of the system. Furthermore, the study elucidates the impact of different kernel functions, revealing that nonlinear kernels provide enhanced performance compared to their linear counterparts within this newly developed theoretical framework. The findings contribute to a deeper understanding of heat and mass transport in fractal tumor geometries and offer a refined modeling approach for advanced predictive bioheat analysis.