Numerical treatment of MHD Al₂O₃-Cu/engine oil-based nanofluid flow in a Darcy-Forchheimer medium: Application of radiative heat and mass transfer laws

This computational study was designed to examine the effect of alumina and copper on the flow of a nanofluid based on engine oil through a Darcy-Forchheimer porous media. The flow model incorporates the generalized radiative heat and mass transport rules. The Darcy-Forchheimer terms in the momentum equation and radiation term in the energy equation are integral parts of the governing nonlinear Navier-Stokes equations, which are two-dimensional partial differential equations. Under the constraint of the convective boundary, the stated PDEs are transformed into highly nonlinear versions of the ordinary differential equations. In order to solve the final ODEs, the numerical RK-45 approach is combined with the shooting methodology. Important aspects of the governing model include porosity, magnetohydrodynamics (MHD), a convective boundary, thermal radiation, and viscous dissipation. The final findings show that when the Forchheimer number increases, the velocity decreases because of the inertial effect included in the flow model. In addition, the velocity profile is improved due to the increased volume percentage of both kinds of nanoparticles. The temperature varies greatly depending on the volume fraction. A higher Biot number and the resulting convective border cause a greater heat flow than a non-convective barrier. For two particular examples, with and without MHD influence, interesting streamlines and contour graphs are produced.