Investigation of time-dependent MHD flow characteristics of Williamson nanofluid across a heated, permeable and inclined stretching sheet within a porous medium

In this work, the unsteady magnetohydrodynamic (MHD) flow of a Williamson nanofluid via a heated, inclined stretching sheet that is permeable and imbedded in a porous media is examined. The present model includes simultaneously buoyancy forces, Joule heating, Dufour-Soret cross-diffusion, heat generation/absorption, an obliquely applied magnetic field and viscous dissipation. The governing nonlinear partial differential equations for momentum, energy and concentration are transformed into a system of coupled ordinary differential equations using similarity variables. For a semi-analytical analysis of this system, the robust Homotopy Analysis Method (HAM) is used in the Mathematica environment. Due to heightened Lorentz resistance, parametric investigation shows that raising the magnetic field inclination from 30° to 60° lowers the primary flow velocity by an estimated 8–19 %. The effect of species-driven energy diffusion is highlighted by the temperature distribution increasing by about 17 % as the Dufour number grows from 0.2 to 0.6. A significant thermo-diffusive mass transfer is demonstrated by the concentration profile escalating by over 25 % as the Soret effect increases from 0.1 to 0.5. On the other hand, the local Nusselt number is boosted by about 60 % when the Prandtl number is raised from 1.0 to 3.0, which greatly improves wall heat transfer. These revelations offer a useful theoretical foundation for maximizing transport efficiency in advanced heat control and material processing systems with porous and inclined configurations employed within intricate multi-physical situations.