Computational analysis of shear dependent heat and mass transfer in MHD hybrid nanofluid within a porous medium

This work numerically investigates enhanced thermal and mass diffusion in an ionized hybrid nanofluid flowing through a permeable medium. The model incorporates modified formulations of thermal and molecular diffusion to address the limitations of their classical counterparts, accounting for non-local and relaxation effects in heat and mass transfer. The hybrid nanofluid consists of copper (Cu) and alumina (Al₂O₃) nanoparticles dispersed in a propylene glycol base fluid. The formulation uniquely combines several advanced mechanisms: shear-dependent diffusivities, ion-slip current and Hall effect, Joule heating, and modified convective boundary conditions. A key innovation is the implementation of velocity gradient-dependent thermal and mass diffusivities, making both heat and solute transport explicitly dependent on local flow conditions. The validity of the generalized diffusion models is confirmed through their reduction to classical laws in limiting cases. A numerical solution to the similarity-transformed equations is obtained via the bvp4c solver in MATLAB. Higher nanoparticle volume fraction and shear-dependent diffusivities enhance heat and mass transfer, whereas magnetic and porous-medium effects suppress them. The Nusselt and Sherwood numbers rise with nonlinear diffusion, emphasizing shear-dominated transport. Results for the local skin friction coefficient, heat transfer rate, and mass transfer rate are presented in tabular form. These results demonstrate how transport processes are governed by the interplay of nonlinear diffusion, magnetic effects, and porous-medium resistance. The application of this work is particularly relevant to systems where magnetic fields interact with fluid flow, such as in cooling systems or filtration devices, where the Hall effect plays a significant role in modifying transport behavior.