Unsteady Darcy Brinkman flow over a semi-infinite flat plate in the presence of thermo diffusion, radiation, and heat source/sink: RSM analysis

This study investigates an unsteady convective flow of a ternary nanofluid (MgO–TiO2–CoFe2O4/H2O) over an infinite vertical plate through Darcy-Brinkman porous medium under the influences of a uniform transverse magnetic field, thermal radiation, Soret effect with different heat source/sinks. The novel contribution of this study lies in examining the effects of suspending ternary nanoparticles on heat and mass transfer in fluid flow. The governing coupled non-linear partial differential equations of the flow model are transformed into ordinary differential equations and solved using perturbation technique. Results reveal that ternary nanoparticles enhance the skin friction coefficient from 0.38% to 0.54%, while the Nusselt number decreases from 0.18% to 0.73%, and the Sherwood number increases significantly from 0.53% to 1.94%. The Soret effect significantly enhances species diffusion, with higher Schmidt numbers reducing molecular diffusion rates. RSM-based predictive models demonstrate excellent accuracy with R 2 values of 97.49% for skin friction, 99.94% for heat transfer, and 96.57% for mass transfer, validated through ANOVA.