Non-linear Velocity Effects on the Flow of Newtonian/Non-newtonian Basefluids with Magnetic/Non-magnetic Nanoparticles over a Stretching Sheet Embedded in a Porous Medium

This article presents a method for numerically modeling how nonlinear velocity affects the flow of Newtonian and non-Newtonian fluids with magnetic or non-magnetic nanoparticles. The flow is generated by a stretchable sheet in a porous medium. We focus on examining the behavior of magnetite and aluminium oxide nanoparticles suspended in water and Sodium Alginate base fluids, respectively. To maintain physical accuracy, we analyze non-Newtonian flow using the Casson model. The model is first converted into a dimensionless form through similarity transformation and then solved using the fourth-order Runge-Kutta method along with a shooting iteration approach. Graphical representations are used to show the impact of different parameters on velocity and temperature distributions. The findings reveal that the velocity profile rises with the shape parameter, and the porosity parameter boosts the temperature profile. Additionally, skin friction is higher when using aluminium oxide nanoparticles in water based fluid, whereas heat transfer rates are higher when using aluminium oxide nanoparticles in a sodium alginate based fluid.