two-phase simulation of magnetohydrodynamics and ferrohydrodynamics impacts on the natural convection of a magnetic nanofluid within a porous cavity

This article attempts to evaluate the impact of magnetohydrodynamics and ferrohydrodynamics on the free convection of a magnetic nanofluid in a square porous cavity. the published literature shows that the magnetic nanofluid convection problems have been mostly simulated by the single-phase model. in the present work, a two-phase model is used to consider the effects of brownian diffusion, thermophoresis, and magnetophoresis of particles. the darcy-brinkman formulation is employed to treat mass, momentum, and energy transport phenomena in the porous medium. the governing equations are solved numerically by the finite volume technique. numerical computations areperformed for various rayleigh numbers (ra =10^4 and ra =10^5 ), hartmann numbers ( 0 ≤ ha ≤ 5), magnetic numbers ( 0 ≤ mn ≤ 4×10^7 ), and porosity ratio of ε = 0.5 and 0.9. the current results are validated via comparison with existing experimental or numerical results in the literature. impacts of magnetohydrodynamics, ferrohydrodynamics, and ferrohydrodynamics/magnetohydrodynamics on the flow field and heat transfer rate are discussed separately in detail by contour plots of streamlines, isotherms, and distribution profiles of nanoparticles. numerical results indicate that at ra =10^4 heat is mainly transferred by conduction and its rate is unaffected by porosity, magnetic, or hartmann numbers. however, at ra =10^6 and ε = 0.9 the average nusselt number decreases by increasing magnetic and hartmann numbers.