Investigation of the two-way movement of Williamson micropolar fluid in a porous medium with consideration of activation energy and thermal radiation

The flow of Williamson fluid over a stretched sheet serves as a model for various real-world scenarios involving the interaction of non-Newtonian fluids with moving surfaces. Its notable practical applications are in the fields of Polymer Processing, Food Processing, and Biomedical Applications. The primary goal of the proposed model is to investigate the effects of Ohmic heating and viscous dissipation on the bidirectional flow of Williamson and micropolar fluids within a porous medium over an extending surface. This study is novel in that it employs the FEM(Finite Element Method) approach to analyze the numerical values of the fluid and thermal characteristics of an incompressible convective flow over a flat surface for the first time. Another novel aspect of this work is the investigation of Arrhenius function terms and magnetic forces in moving fluid flow. Heat convection and velocity slip at the surface are also examined. The mathematical model of the problem results in higher-order, nonlinear ordinary differential equations through the appropriate combination of variables. The Finite Element Method is used to solve the given nonlinear system of differential equations. The present study has revealed several significant insights, notably that skin friction increases with the enhancement of porosity, as well as the characteristics of Williamson fluids and micropolar fluids. Flow patterns are analyzed and visualized by examining and graphing various components that result from the analysis. As the slip parameter increases, the velocity field decreases in the x-direction. As the heat transfer of the Williamson fluid flowing over the stretched sheet increases at k = 3, its velocity is approximately 45.55 % greater compared to the k = 1 case under the lowest heat transfer condition. The velocity in the x-direction decreases as the slip parameter increases. Additionally, it has been observed that the concentration of the Williamson fluid decreases, while the temperature distribution increases with higher Eckert number values.