Analysis of bidirectional flow of Williamson micropolar fluid in porous medium with activation energy and thermal radiation

The prime objective of the proposed model is to explore the impacts of viscous dissipation and Ohmic heating on the bidirectional flow of micropolar and Williamson fluids in porous medium over a stretching surface. The velocity slips and heat convection are assessed at the surface as well. The concernment of chemical reaction, thermophoresis, and Brownian motion repercussions is also considered. More complex nonlinear ordinary differential equations arise when the variables are combined in a suitable manner to represent the mathematical model of the problem. The Galerkin weighted residual approach is used to solve non - linear differential equations' system that has been developed. Flow patterns are presented by utilizing multiple plots and assessing the influence of various emerging factors. Tables are frequently utilized to characterize the rates of mass and heat transfer. The current findings have yielded several important crucial findings, including the fact that skin friction improves with improvements in the porosity, Williamson fluid, and micropolar fluid parameters. The Nusselt number decays with increments in Eckert numbers and heat source parameters. The velocity field speeds up in the x-direction as the slip parameter enhances, but it lessens in both directions with rise in the porosity parameter and the Williamson fluid parameter. The microrotation velocity profiles in both directions experience a significant reduction as the microrotation slip parameter increases. Also, it has been noted that the nano-liquid concentration profile becomes lesser while the temperature distribution becomes higher for higher values of the Eckert numbers. The thermal profile accelerates as the heat source parameter increases.