Thermal energy optimization in Darcy-Forchheimer slip flow featuring viscoplastic (Casson) model subjected to diffusion of chemically reactive species

This study investigates the Darcy–Forchheimer magnetic field driven flow of a viscoplastic (Casson) fluid over a vertical stretchable surface. Effects of thermal radiation, Joule heating, heat generation/absorption and first-order chemical reaction are incorporated in transport expressions. Dual stratification consideration delineates wall conditions modifying subject to ambient liquid while slip features permit partial slip (velocity and thermo-solutal) on the stretchy surface. The governing nonlinear boundary-layer equations are transformed using similarity variables and solved numerically by implementing bvp4c scheme. The results reveal that velocity decreases with higher porosity, material, magnetic field and velocity slip factors while temperature is enlarged by thermal radiation, stratification, heat source and Eckert number. Concentration is reduced with larger Schmidt number, solutal slip, and chemical reaction parameters. Furthermore, the Nusselt number decreases with radiation, stratification, and slip, whereas the Sherwood number increases with Schmidt number and chemical reaction factor. These findings provide useful insights for designing efficient thermal-fluid systems in polymer processing, coating technologies, and other industrial applications involving viscoplastic fluids.