Numerical and ANN Modeling of Three-Dimensional Cross Tri-Hybrid Nanofluid Flow in Porous Tumor Tissue for Hyperthermia Applications

The present study investigates the three-dimensional Darcy–Forchheimer flow and thermal transport of a Cross tri-hybrid magnetic nanofluid through porous tumor tissue under hyperthermia conditions. The proposed mathematical formulation incorporates important biomedical transport mechanisms, including magnetohydrodynamic interaction, nonlinear porous resistance, thermal radiation, viscous dissipation, Joule heating, and internal heat generation associated with localized cancer hyperthermia therapy. The governing nonlinear partial differential equations are transformed into a coupled system of ordinary differential equations using suitable similarity transformations and solved numerically through MATLAB’s bvp4c technique. In addition, a multilayer neural network (MLNN)-based predictive framework trained using the Levenberg–Marquardt algorithm is employed for rapid approximation of the nonlinear thermofluid behavior. The obtained results reveal that magnetic effects suppress excessive nanoparticle transport through Lorentz-force-induced momentum damping while simultaneously enhancing localized thermal energy through Joule heating, thereby supporting controlled thermal retention within the tumor region. The Darcy and Forchheimer resistance mechanisms significantly regulate fluid penetration and nanoparticle residence time inside the porous biological structure, whereas thermal radiation and viscous dissipation enhance thermal energy transport and increase the thermal boundary layer thickness. Furthermore, the tri-hybrid nanofluid exhibits superior thermofluid performance compared with the blood-based fluid model by improving the primary and secondary skin-friction coefficients by approximately 9.95% and 9.50%, respectively, with only a slight reduction in heat transfer rate. The MLNN predictions show excellent agreement with the numerical bvp4c solutions, yielding low mean squared error and regression coefficients approaching unity. The present findings provide useful insight into controlled thermal regulation and hyperthermia-assisted targeted drug delivery systems for advanced biomedical applications.