Multiphysics Finite Element Analysis of Diffusive–Bioconvective MHD Hybrid Nanofluid Flow Over an Exponentially Stretching Sheet

This study examines the diffusive–bioconvective magnetohydrodynamic (MHD) flow of a hybrid nanofluid past an exponentially stretching sheet embedded in a porous medium, incorporating thermal radiation, viscous dissipation, Soret–Dufour effects, and gyrotactic microorganisms. The hybrid nanofluid, consisting of nanoparticles (Ag + TiO2) suspended in water, is employed to enhance thermal conductivity and overall heat transfer performance. The governing nonlinear partial differential equations for the incompressible, steady, and two-dimensional flow are transformed into a system of ordinary differential equations via appropriate similarity variables and solved numerically using the finite element method (FEM). Comprehensive parametric analyses reveal that the fluid velocity decreases with increasing magnetic field strength and suction parameter, while it rises under the influence of viscous dissipation, thermal radiation, and the Dufour effect. The temperature field is significantly augmented by thermal radiation, viscous dissipation, and coupled Soret–Dufour mechanisms. The concentration field diminishes with stronger chemical reactions and higher Lewis numbers but grows with the Soret effect. Furthermore, skin friction coefficient increases notably with magnetic field intensity, viscous dissipation, and Soret–Dufour parameters. Both the local Nusselt number and Sherwood number exhibit declining trends with rising heat generation and chemical reaction rate, respectively. The computed results demonstrate excellent agreement with established benchmark solutions.