Coupled Thermal-Solutal Transport in Williamson Nanofluids with Oblique Magnetic Fields and Spatially Graded Porosity

Motivated by the need to enhance heat and mass transfer in advanced engineering and biomedical systems, this study investigates the complex behavior of an incompressible Williamson nanofluid subjected to an oblique magnetic field over a stretchable surface. The flow is assumed to occur through a porous medium, incorporating the graded permeability of the porous material, and is influenced by multiple physical mechanisms including thermal radiation, internal heat generation or absorption, and nanoparticle migration due to Brownian motion and thermophoresis. In addition, the fluid contains a chemically reactive species governed by Arrhenius activation energy. To accurately capture microscale interfacial effects, slip boundary conditions for velocity, temperature, and concentration are applied at the wall. Similarity analysis of regulating equations yields a coupled system of non-linear ordinary differential equations (ODEs) describing the boundary layer flows. MATLAB's bvp4c solver performs numerical integration for this system with strict convergence criteria by using initial values that respect physical realism. Numerical results indicate that increasing the Hartmann number results in approximately an 18% increase in the surface friction coefficient, whereas thermophoretic effects reduce the Nusselt number by 12–15%, thus resulting in a reduction of thermal transport efficiency. Numerical code has been validated against previous benchmark solutions with relative deviations less than 1.2%, demonstrating the robustness and accuracy of the numerical procedure implemented in this study. Practically, these findings assist with advanced application improvements, like cooling machines in mining and petroleum exploration, polymer sheet extrusion, and nanofluid thermal management systems, that require precise control of non-Newtonian flow and coupled transport processes.