Thermal radiation and diffusion effects on MHD sisko fluid flow over a nonlinearly stretchable porous sheet

This research delves into the intriguing dynamics of a magneto-Sisko fluid within a two-dimensional realm, shaped by the influence of a nonlinearly stretchable sheet nestled in a porous medium. The investigation embraces the impacts of a steady magnetic field, thermal radiation, and heat generation, while artfully weaving in the phenomena of Brownian motion and thermophoresis diffusion. By applying a similarity transformation, the governing nonlinear partial differential equations morph into ordinary differential equations, which are deftly tackled using the Newton-Raphson shooting method in tandem with the Runge-Kutta-Fehlberg algorithm. The outcomes indicate that an increase in the Sisko fluid parameter amplifies velocity profiles, concurrently diminishing both temperature and concentration distributions. For example, elevating the Sisko parameter from 1.0 to 2.0 propels the velocity profile upward by approximately 20%, while the temperature and concentration profiles witness reductions of 10% and 8%, respectively. Moreover, escalating values of the power-law exponent and the nonlinear stretching coefficient contribute to a decline in velocity, temperature, and concentration. In particular, when the power-law index ascends from 1.2 to 1.8, the velocity experiences a decrease of 14%, and temperature and concentration diminish by 12% and 5%, respectively. The introduction of thermal radiation enhances the temperature profile by nearly 20%, underscoring its pivotal role in the transport of energy. These results resonate with prior research, highlighting the intricate dance of magnetic fields, viscosity fluctuations, and heat diffusion mechanisms in shaping the fluid's behavior. The findings furnish invaluable perspectives for refining industrial applications such as polymer extrusion, metallurgical endeavors, and chemical engineering systems.