Dynamics of activation energy and gyrotactic microorganisms on radiative Williamson nanofluid with Soret and Dufour bounded by porous nonlinearly stretching surface

Cross-diffusion refers to the simultaneous diffusion of multiple species within a mixture, a phenomenon that portrays a precarious role in various material, environmental and industrial system. This investigation focuses on inspecting the impressions of cross-diffusion on electromagnetics Williamson nanofluid flowing over due to nonlinearly stretching flat surface. The flow is bounded by Darcy-Forchheimer porous medium. The study carefully considers the opposing appearances of motile microorganisms, Soret, and Dufour phenomena. For motivation of problem the influence of Brownian diffusion thermal radiation and thermophoresis have been taken into account. Similarity transformations are used to transform nonlinear partial differential equations of governing system into ordinary differential equations. These ODEs are then integrated numerically using ND solve command in MATHEMATICA and bvp4c function of MATLAB combined with the shooting approach. The outcomes reveal that the speed of fluid decreases with higher porosity factors and stronger magnetic fields. Higher Prandtl number, causes a deceleration in the temperature profile, but increases with increased thermophoresis, enhanced Brownian motion and higher radiation levels. The concentration profile is enhances with greater activation energy and stronger Soret number. The accuracy of present outcomes a comparisons with previous literature is and shows outstanding agreement.