Thermal Radiation Effects on 2D Stagnation Point Flow of a Heated Stretchable Sheet with Variable Viscosity and MHD in a Porous Medium

This paper proposes a mathematical modeling approach to examine the two-dimensional flow stagnates at $x=0$ over a heated stretchable sheet in a porous medium influenced by nonlinear thermal radiation, variable viscosity, and MHD. This study’s main purpose is to examine how thermal radiation and varying viscosity affect fluid flow motion. Additionally, we consider the convective boundary conditions and incorporate the gyrotactic microorganisms equation, which describes microorganism behavior in response to fluid flow. The partial differential equations (PDEs) that represent the conservation equations for mass, momentum, energy, and microorganisms are then converted into a system of coupled ordinary differential equations (ODEs) through the inclusion of nonsimilarity variables. Using MATLAB’s built-in solver bvp4c, the resulting ODEs are numerically solved. The model’s complexity is assessed by plotting two-dimensional graphics of the solution profiles at various physical parameter values. The physical parameters considered in this study include skin friction coefficient, local Nusselt number, local Sherwood number, and density of motile microorganisms. These parameters measure, respectively, the roughness of the sheet, the transformation rate of heat, the rate at which mass is transferred to it, and the rate at which microorganisms are transferred to it. Our study shows that, depending on the magnetic parameter M, the presence of a porous medium causes a significant increase in fluid velocity, ranging from about 25% to 45%. Furthermore, with an increase in the Prandtl number $Pr$, we have seen a notable improvement of about 6% in fluid thermal conductivity. Additionally, our latest findings are in good agreement with published research for particular values. This study provides valuable insights into the behavior of fluid flow under various physical conditions and can be useful in designing and optimizing industrial processes.