Aspects of Dual Simulation for Modified Thermal Flux Advances in Non-Newtonian Reiner–Philippoff Fluid Flow past a Shrinking Plate Embedded in a Porous Medium

This study investigates the effects of non-Newtonian Reiner–Philippoff fluids on porous media, particularly in the context of steady radiative mixed convection flow and heat transfer near a shrinking plate surface in the presence of magnetohydrodynamics (MHD). The mathematical model is constructed using PDEs and transformed into ODEs via similarity transformations, with numerical solutions obtained using MATLAB’s bvp4c function. The results demonstrate that boundary layer separation occurs slowest for dilatant fluids and fastest for pseudoplastic fluids, with Newtonian fluids exhibiting moderate separation rates. Thermal radiation and media porosity parameters are found to reduce heat transfer by approximately 0.95% and 0.02%, respectively, while accelerating boundary layer separation. Conversely, magnetic effects and suction parameters increase heat transfer by about 0.08% and 4.25%, respectively, enhancing both fluid velocity and temperature. The mixed convection parameter indicates the possibility of dual solutions, with the opposing flow favoring this phenomenon more than the assisting flow. The time-based stability analysis reveals that the first solution is stable, whereas the second solution is unstable. These findings provide significant insights into the behavior and control of Reiner–Philippoff fluids in practical applications involving porous media and magnetic fields.