Bio-convective flow of non-Newtonian Williamson nanofluid model with heat generation and thermal radiation aspects past over a stretched porous sheet via OHAM

In this research, we conducted a thorough study of Williamson fluid flow in three dimensions over a stretchable sheet with linear permeability, incorporating the influence of heat radiation. The nonlinear governing equalities were figured out utilizing the OHAM. Our findings elucidate the significant impact of various parameters, including the Bioconvection Lewis number, Peclet factor, Williamson, heat radiation and porosity parameters, thermophoresis number, Brownian factor, Prandtl component towards temperature, concentration, and velocity distributions. The study reveals that the velocity in \(x\) $x$ and \(y\) $y$ -directions falls with the rise in Williamson and porosity parameters The numerical analysis further demonstrates the influence of these factors on surface drag force, revealing trends such as reduced surface drag force with increasing porosity parameters, and an augmented surface drag force with increasing Williamson parameter. Additionally, enhancement in heat generation and thermal radiation parameters it increases the temperature distribution. Similarly, rise in Brownian number and thermophoresis parameters that lead to enhancement in temperature profile.