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


1 School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

2 Head of Automobile Engineering Department, Al-Musayab College for Engineering and Technology, Babylon University, Babylon Province, Iraq


The problem of 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 is studied numerically using finite element method. The left vertical wall is maintained at a constant hot temperature $T_{h}$ and the right vertical wall is maintained at a constant cold temperature $T_{c}$, 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 specified boundary conditions. The governing parameters of this study are the Rayleigh number $(10^{3}leq Ra leq10^{7})$, Darcy number $(10^{-5}leq Da leq10^{-3})$, the fluid layer thickness $(0.4leq S leq0.8)$ and the inclination angle of the cavity ($0^{circ} leq omega leq 60^{circ}$). The results presented for values of the governing parameters in terms of streamlines in both nanofluid/fluid-layer, isotherms in both nanofluid/fluid-layer and average Nusselt number. 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 convection