Brownian and thermophoresis effects on Williamson hydromagnetic fluid flow past a porous plate with heat and mass flux: SRM analysis

The present investigation analyses the Brownian diffusion and thermophoretic effects influence the motion and thermal–mass transport characteristics of an electromagnetic free, convective, radiative, and chemically reacting Williamson fluid flow over an inclined porous surface. The novelty of this investigation lies in considering the effects of chemical reaction, heat source/sink and Brownian motion on flow, heat and mass transfer with two boundary conditions: (i) Prescribed surface temperature and surface mass (PST & PSM), and (ii) Prescribed heat and mass flux (PHF & PMF). The complex nonlinear coupled partial differential equations are transformed into ordinary differential equations using similarity transformations and solved numerically through the BVP4C solver on MATLAB, with outcomes presented via tables and graphical illustrations, while Surface Response Methodology (SRM) is applied to analyze parameter sensitivity. Results reveal that Browinan motion, thermophorosis, radiation and heat source parameters enhance the temperature on both the PST and PHF cases but reverse phenomenon is observed with Weissenberg number, whereas as Biot number elevates temperature and concentration profiles. The statistical accuracy of skin friction prediction is high, with R² values of 98.39% and 98.92% for Cases 1 and 2, respectively. Furthermore, the Nusselt number exhibits greater sensitivity to thermal radiation and the Weissenberg number compared to the heat source parameter.