Thermomagnetically Driven Ferrofluid Layer Saturating a Porous Medium over a Stretching Sheet under a Weak Field Gradient, Radiation and Viscous Dissipation

In this study, we analyze laminar ferrofluid flow and heat transfer above a linearly stretching sheet embedded in a homogeneous, isotropic porous medium. The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution, utilizing a comprehensive semi-analytical approach. The model retains a genuine ferrofluid signature through a weak, externally imposed magnetic-field gradient that generates a Kelvin (thermomagnetic) body force while avoiding full magnetostatic complexity. Porous resistance is represented by the Brinkman–Darcy –Forchheimer framework; thermal radiation is included via the Rosseland diffusion approximation linearized about the ambient temperature; and viscous dissipation is accounted for. A classical similarity transformation converts the boundary-layer equations into coupled, nonlinear ordinary differential equations for the reduced stream function and temperature. The reduced system is solved via a semi-analytical scheme based on the Homotopy Perturbation Method (HPM). Consistency and limiting behavior are verified: the model reduces smoothly to the clear-fluid non-magnetic case, and the energy equation recovers the non-radiative and/or adiabatic limits. The compact similarity structure, together with the closed-form HPM corrections, provides a transparent platform for systematic parametric studies of thermomagnetically driven ferrofluid boundary layers in porous media, enabling clear isolation of the roles played by porosity, inertial drag, radiation, viscous heating, and weak magnetic-gradient forcing in both velocity and thermal fields.