The Interplay of Microorganisms and Magnetohydrodynamics: Effects on Williamson Fluid Flow Across Different Boundary Conditions

This article explores the implications of varying properties in MHD Williamson fluid flow, which includes gyrotactic bacteria, under two different boundary conditions: a permeable stretching sheet and a melting surface. It takes into consideration different Prandtl and Schmidt values for both mass and gyrotactic bacteria, as well as factors acting as temperature, concentration, velocity of first and second order, microbe slippage, porous medium, and non-linear chemical processes. The study investigates how physical parameters affect velocity, heat, mass, and microorganism profiles by converting the governing PDEs for momentum equation, heat equation, mass, and microorganism equations into non-linear coupled ordinary differential equations. These equations are then solved numerically using the bvp4c solver. The findings indicate that while the thermal heat transfer rate, concentration rate, and microorganism boundary layer thickness are positively influenced by the porosity parameter and magnetic field parameter, they have a negative impact on the velocity profile and momentum boundary layer thickness. Williamson fluid parameter ( \(We\) $\mathit{We}$ ) and porosity parameter (Kp) increases, coefficient of skin friction oscillates, local Nusselt number, local Sherwood number and local density number of the motile microorganisms decreases. All the parameters are having higher influence in melting surface as compared to permeable surface.