Hydromagnetic stagnation point flow of a magnetite ferrofluid past a convectively heated permeable stretching/shrinking sheet in a Darcy–Forchheimer porous medium

In this study, a two-dimensional magnetohydrodynamic stagnation point flow of magnetite ferrofluid past a stretching/shrinking sheet through a Darcy–Forchheimer porous medium is investigated in the occurrence of viscous dissipation, suction/injection, and convective heating. Using appropriate similarity transformations the governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations, and then solved numerically using the shooting technique. Numerical results are obtained for dimensionless ferrofluid velocity, ferrofluid temperature, skin friction, and Nusselt number. The effects of various physical parameters on these quantities are investigated and presented in graphs and tables. The results indicate that dual solutions exist for the shrinking sheet. Stability analysis is performed to identify the stable solutions. It is found that the upper branch solution is hydrodynamically stable and physically achievable, whereas the lower branch solution is unstable and physically unrealistic. The fluid flow stability is maintained by increasing the magnetite nanoparticle volume fraction, suction/injection, and the magnetic field parameter. On the contrary, the porous medium parameter and porous medium inertia parameter inflates the flow stability. The heat transfer rate intensifies with the magnetite nanoparticle volume fraction and reduces with the porous resistance term.