Computational investigation of magnetohydrodynamics Casson Micropolar fluid flowing past a permeable linearly stretchy wall with heat source

In this study, a computational investigation that analyze the behavior of Magnetohydrodynamic (MHD) micropolar Casson fluid flowing via a linearly stretchy wall, considering the effects of heat source in a permeable medium. To achieve this, a similarity transformation is adopted, to convert the fundamental partial differential equations into nonlinear ordinary differential equations which are then solved numerically using collocating weighted residual scheme that adopts Hermite polynomials as the basis functions and Gauss-Lobatto points for spatial discretization. To affirm the accuracy of the simulation, the outputs are validated using 4th order Runge-Kutta method via shooting technique serving as the control method with the aid of Mathematical software (Maple 18.0). This approach enables the numerical solutions for the velocity \bar{f}^{\prime}; temperature \bar{\theta}, and microstructure \bar{g} of the fluid. The results are then presented in tabular and graphical forms, allowing for a detailed assessment of the impact of various parameters on the fluid's behavior. It is deduced that, increased porosity enhances thermal dispersion, reduces thermal resistance, and promotes heat transfer. Also, as magnetic field (M) increases, the temperature profile exhibits significant enhancement, primarily as a result of viscous heating, resulting in improved temperature at the wall. As the viscous dissipation activity enhances, the heat profile also improves as a result of steady growth in the heat boundary layer. Through the comprehensive analysis of the graphical results, the relationship between these parameters and the fluid's behavior were properly observed, shedding light on the underlying physical mechanisms. This study establishes the influence of fluid mobility and Eckert number on thermal profiles, providing critical implications for industrial heat transfer optimization and fluid flow management and contributing to a depth understanding of the complex dynamics of MHD Casson fluid flow in porous media with potential applications in different fields of engineering and physics.