Краткое описание

Two-dimensional steady natural convection in a porous cavity, bounded both by isothermal vertical walls at different temperatures and adiabatic horizontal ones, has been numerically studied. A generalized model for the momentum equations was employed. Non-Darcian effects were taken into account in the momentum equations, the thermal dispersion effect and the variable stagnant thermal conductivity were included in the energy equation, and the wall effect on porosity variation was approximated by an exponential function. The governing equations in terms of the primitive variables were numerically solved by the finite-volume method using a staggered variable arrangement, and the pressure-velocity coupling was treated by the PRIME algorithm. The influence of the inertial, Brinkman's, and Forchheimer's terms was compared to the experimental and numerical Nusselt numbers available in the literature. The numerical results indicate that the generalized model with thermal dispersion reduces the discrepancy in the experimental results for Prandtl numbers ranging from 7.1 to 480 for a high modified Rayleigh number; while for a low modified Rayleigh number, the thermal dispersion term is not appropriate. Two correlations were also proposed in order to evaluate the average Nusselt number, considering the thermal dispersion: one for a tall cavity and another for a shallow cavity.