Heatlines Analysis of Natural Convection in an Enclosure Divided by a Sinusoidal Porous Layer and Filled by Cu-Water Nanofluid with Magnetic Field Effect

A numerical study is executed to analyze the steady-state heatlines visualization, fluid flow, and heat transfer inside a square enclosure with the presence of the magnetic field. The enclosure is divided into three layers, the right and left layers are filled with (Cu-Water) nanofluid while the center layer is sinusoidal porous and filled with the same nanofluid. Constant hot and cold temperature is applied to the right and left walls, respectively, the top and bottom walls are adiabatic. Galerkin finite element approach based on weak formulation is applied to solve the governing equations. The parameters studied are the number of undulation (N=1, 2 and 3), Rayleigh number (103≤Ra≤106), Darcy number (10-5≤Da≤10-1), Hartmann number (0≤Ha≤100) and volume fraction (0≤φ≤0.06). Three cases were provided depending on the number of undulations of the porous medium layer. The results obtained that the absolute value of the maximum stream function decreases with the increase of the Hartmann number and the decrease of the Darcy number for all three cases of the wavy porous layer. Heatlines and isothermal lines increase as the Darcy number is increased. The average Nusselt number grows by increasing the Rayleigh number and decreasing the Hartmann number. The enhancement of heat transfer occurred for case (2) as the Darcy number increased at a constant Ra=105, Ha=40. Also, It can be concluded that there was an excellent agreement between this study and those of Hamida and Charrada, by an approximately maximum absolute error of 2.062%.