Prediction of natural convection flow using a network model and numerical simulations inside an enclosure with distributed solid blocks

Steady state natural convection of a fluid with Pr &asyum; 1 within a square enclosure containing uniformly distributed, conducting square solid blocks is investigated. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The natural convection flow is predicted employing the nondimensional volumetric flow rate ( Q-{max }{*}) by using a network model and also using numerical simulations. For identical solid and fluid thermal conductivities (i.e. k s = k f ), a parametric study of the effect of number of blocks (N 2), gap size (δ) and enclosure Rayleigh number (Ra) on Q-{max }{*} is performed using the two approaches. Network model predictions are observed to agree well with that from the simulations until Raδ3 ∼ 12. Considering the enclosure with blocks as a porous medium, for a fixed enclosure Ra number, increasing the number of blocks for a fixed volumetric porosity leads to a decrease in enclosure permeability, which in turn reduces the flow rate. When the number of blocks is fixed, and for a given Ra number, the flow rate increases as the porosity increases by widening the gap between the blocks.