Numerical analysis of flow and natural convection heat transfer in a circular enclosure heated from bottom utilizing porous layer

In the present paper, simulation of laminar natural convection heat transfer of 〖Fe〗_3 O_4 -water nanofluid in a circular enclosure has been carried out numerically using Buongiorno two phase model. A porous layer is inserted into the hot wall of the enclosure and applied constant external magnetic field caused to MHD effect in the cavity. The simulations are performed utilizing two phase model and nanoparticle concentration distribution is presented. All of the equations are solved in dimensionless form. Influence of the porous layer existence on heat transfer enhancement nanofluid flow is studied. The control parameters in this study are Darcy number (1e-6 ≤Da≤1e-1), angle of applied magnetic field (0≤γ≤90), Hartmann number (0≤Ha≤200), effective conductive heat transfer coefficient of porous layer ( 10≤k_eff≤100), Rayleigh number ( 1e3≤Ra≤5e5), geometrical parameters like porous layer thickness (0.01 ≤t_Layer≤0.09) and central angle of cavity (0≤θ≤90). The gained results which are derived in form of plots, contours and streamlines show the dependency of Nusselt number to control parameters. According to the results, any changes in Darcy number causes to Nusselt number variations and also there is a specified Darcy number that heat transfer reduces by increase of Darcy number. Moreover, by increment of Hartmann number, leading to higher Lorentz force, the average Nusselt number will reduce because the momentum of fluid flow and consequently convective heat transfer decrease inside the enclosure.