Darcian Natural Convection in Inclined Square Cavity Partially Filled Between the Central Square Hole Filled with a Fluid and Inside a Square Porous Cavity Filled with Nanofluid

The problem of darcian natural convection in inclined square cavity partially filled between the central square hole filled with fluid and inside a square porous cavity filled with nanofluid is numerically studied using the finite element method. The left vertical wall is maintained at a constant hot temperature Th and the right vertical wall is maintained at a constant cold temperature Tc, while the horizontal walls are adiabatic. The governing equations are obtained by applying the Darcy model and Boussinesq approximation. COMSOL’s finite element method is used to solve the non-dimensional governing equations together with the specified boundary conditions. The governing parameters of this study are the Rayleigh number (103 ≤ Ra ≤ 107), the Darcy number (10−5 ≤ Da ≤ 10−3), the fluid layer thickness (0.4 ≤ S ≤ 0.8) and the inclination angle of the cavity (0◦ ≤ ω ≤ 6 0◦). The results for the values of the governing parameters in terms of the streamlines, isotherms and average Nusselt number will be presented. The convection is shown to be inhibited by the presence of the hole insert. The thermal property of the insert and the size have opposite influence on the convection. The results have possible applications in heat-removal and heat-storage fluid-saturated porous systems.