Numerical Investigation of the Influence of a Magnetic Field on the Laminar Flow of a Yield-Stress Nanofluid over a Backward Facing Step

The present study focuses on the flow of a yield-stress (Bingham) nanofluid, consisting of suspended Fe3 O4 nanoparticles, subjected to a magnetic field in a backward-facing step duct (BFS) configuration. The duct is equipped with a cylindrical obstacle, where the lower wall is kept at a constant temperature. The yield-stress nanofluid enters this duct at a cold temperature with fully developed velocity. The aim of the present investigation is to explore the influence of flow velocity (Re = 10 to 200), nanoparticle concentration (ϕ = 0 to 0.1), magnetic field intensity (Ha = 0 to 100), and its inclination angle (γ = 0 to 90) and nanofluid yield stress (Bn = 0 to 20) on the thermal and hydrodynamic efficiency inside the backward-facing step. The numerical results have been obtained by resolving the momentum and energy balance equations using the Galerkin finite element method. The obtained results have indicated that an increase in Reynolds number and nanoparticle volume fraction enhances heat transfer. In contrast, a significant reduction is observed with an increase in Hartmann and Bingham numbers, resulting in quasi-immobilization of the fluid under the magnetic influence and radical solidification of this type of fluid, accompanied by the suppression of the vortex zone downstream of the cylindrical obstacle. This study sheds light on the complexity of this magnetically influenced fluid, with potential implications in various engineering and materials science fields.