Free convection heat transfer in a square cavity filled with a porous medium saturated by a nanofluid

The steady natural convection in a two-dimensional porous square cavity filled with a nanofluid and including internal heat generation is presented in this paper. The mathematical model considered consists of the Darcy equation for the momentum, while a new model is proposed for the energy and nanoparticles' concentration equations. The system of partial differential equations is written in terms of a dimensionless stream function, temperature and concentration of the nanoparticles and is solved numerically using the finite difference method. The effects of the governing parameters, such as: Rayleigh number Ra, the Lewis number Le and the dimensionless ratio between the thermophoretic and Brownian coefficients N-BT on the velocity, temperature and nanoparticles' concentration, Nusselt and Sherwood numbers are studied. It is found that the addition of the nanoparticles into the fluid saturated porous medium reduces the temperature and enhances the heat transfer when the value of the thermal conductivity of the nanoparticles is much higher than the thermal conductivity of the solid structure of the porous medium. This addition has almost no effect on the flow and heat transfer characteristics when the values of the thermal conductivity of the nanoparticles and the thermal conductivity of the solid structure of the porous medium have close values. (C) 2015 Elsevier Ltd. All rights reserved.