Numerical Investigation of Maxwell Dusty Fluid Flow Over a Porous Medium With Variable Thermal Conductivity

ABSTRACT This research formulates a two‐phase mathematical model to investigate the dynamics of a Maxwell dusty fluid across a linearly stretching surface embedded within a Darcy–Forchheimer porous medium, influenced by a magnetic field and varying thermal conductivity. Dusty fluid flows are significant in industries such as oil transportation, gas cleaning, and car exhaust control. The governing partial differential equations are reduced to a system of ordinary differential equations using similarity transformations and solved numerically via the bvp4c solver in MATLAB. The model's reliability is verified by comparing its results with previously published results. Parametric analysis reveals that increasing the magnetic field strength, Maxwell fluid parameter, and Forchheimer number decreases the velocities of both the fluid and dust phases, while increasing the temperature. The dusty‐phase temperature is more sensitive to thermal conductivity and fluid–particle interactions. The local Nusselt number increases with thermal conductivity but drops with magnetic and Maxwell parameters, implying a lower heat transfer rate. These findings provide a deeper scientific understanding of how viscoelastic particulate flows transmit heat and momentum.