Steady natural convection in open cavities filled with a porous medium utilizing Buongiorno's nanofluid model

In this paper, a numerical study is performed for the steady natural convection inside an open enclosure filled with a porous medium using nanofluid. The two phase model is applied for the nanofluid and the Darcy number for the porous medium. The governing partial differential equations are solved numerically using the Galerkin finite element method with Q(2)/P-1(disc) element and valuable comparisons are performed. The computations are produced for wide ranges of the governing parameters, i.e. Rayleigh number Ra from 10(4) to 10(7), Darcy number Da from 10(-2) to 10(-6), Lewis number L from 0.1 to 1, buoyancy ratio Nr from 0.1 to 1 and Nb from 0.1 to 1. It is found that the average heat transfer rate is a decreasing function of the Lewis number and the buoyancy ratio for high values of Rayleigh number.