THEORETICAL ANALYSIS OF MHD DARCY–FORCHHEIMER POROUS MEDIA FOR HYBRID NANOMATERIAL FLOW WITH THIRD-GRADE FLUID OVER AN EXPONENTIAL STRETCHING SHEET

This study explores the flow of an electrically conducting hybrid nanofluid within a Darcy–Forchheimer porous medium (PM), past an exponentially stretching sheet, using fractal dimensions. The analysis operates a third-grade non-Newtonian fluid model to replicate the thermal activities of a hybrid nanofluid based on Al₂O₃-Cu/water. The study observes the thermal proficiency of cylindrical-shaped nanoparticles under the impact of an externally applied magnetic field. The suggested model is simulated utilizing the highly efficient and rigorous solver bvp4c. The correlation between the viscosity of the hybrid nanofluid and the base fluid is elucidated using a fractal formula. The outcomes indicate that the velocity field diminishes as the magnetic field parameter, third-grade fluid parameter, porosity parameter, cross-diffusion parameter, and volume fractions of alumina and copper nanoparticles increase. It is detected that an increase in the viscoelastic parameter indicates an equivalent rise in the velocity distribution. The results also indicate that the Nusselt number rises with the Forchheimer number but declines with a higher Prandtl number. The study shows that the skin friction coefficient rises with both the Forchheimer number and the Prandtl number. Moreover, the Sherwood number is detected to increase with higher values of the Forchheimer number and Prandtl number. The validity of the suggested model is verified by comparing the solutions with existing published data, presenting excellent agreement. This concordance emphasizes the accuracy and consistency of the results obtained in this study.