This study examines non-Newtonian nanofluid flow with heat transfer via a non-Darcy porous medium in the presence of effects. Additionally, the effects of the heat source, viscous and Ohmic dissipation, chemical reaction, electromagnetic field, and Biot number are taken into account. The non-linear equations that control the flow can be made simpler by using appropriate similarity transformations. Then, using a shooting and matching approach, the Rung-Kutta-Merson method is utilised to derive numerical solutions for the velocity, temperature, and concentration of nanoparticles as functions of the problem's physical parameters. This analysis could lead to the development of a model that could help in the understanding of the mechanics of physiological fluids. Additionally, the implications of these parameters on these solutions are studied numerically and graphically. It is discovered that as the Biot number rises or falls, both tangential and normal velocities change. While the temperature increases or decreases as the pressure gradient and radiation parameters increase, the concentration of nanoparticles increases or decreases as the Schmidt numbers and magnetic field parameters increase.