NUMERICAL STUDY OF NATURAL CONVECTION IN A 2-D SQUARE CAVITY WITH FLUID-POROUS MEDIUM INTERFACE AND HEAT GENERATION

A numerical study was performed regarding two-dimensional natural convection in a square cavity that contains two horizontal regions formed by a homogeneous fluid and an isotropic heat-generating porous medium. The one-domain formulation was used for developing the mathematical model, with a binary parameter so as to the momentum and energy equations were valid throughout the domain. The governing equations were discretized using orthogonal collocation and the set of algebraic equations generated is solved via Newton method. The simulations were performed for Rayleigh numbers among 10(3) and 10(6) for values of the dimensionless heat Source (S-0) of 0, 10, 30 and 50; Darcy numbers of 10(-4), 10(-6), and 10(-8) and for positions of the porous medium-fluid interface between 0 <= Y-p <= 1, considering the Prandtl number equals to 0.71, to assess their effect on the streamlines, isotherms and Nusselt number. In addition, this method was compared with previously published reports with good agreement. The results indicate that the one-domain formulation is a good approximation for predicting the flow between the two phases without the requirement to specify interfacial conditions.