The increasing potential of Eyring-Prandtl fluid lies in its applications in heat and mass transfer. The current analysis holds significant promise, particularly in scenarios where non-Newtonian working fluids are utilized. This research aids in optimizing industrial processes, designing of efficient cooling systems in electronic devices, and in polymer and food processing. Methodology: The similarity transformations are utilized to turn a set of partial differential equations (PDEs) into a system of ordinary differential equation (ODE). The resulting system is modified and effectively solved by mean of numerical method known as the Runge Kutta method with bvp4c in MATLAB. Outcomes: Graphical results show the behavior of several physical parameters across boundary layers of buoyancy assisting and buoyancy opposing region. The magnetic field enhances the thermal conductance of the fluid flow that give rise to flow rate at the surface as well as within the boundary layers. The existing outcomes in the study are attained as a special case of current study. Eyring-Prandtl fluids, with their unique rheological properties can improve the design and efficiency of microfluidic systems used in various applications such as chemical synthesis, drug delivery, and biomedical diagnostics.