Natural convection in horizontal-layered porous annuli

Numerical results are reported for natural convection in a horizontal porous annulus comprising two sublayers. Attention is focused on the effects of permeability contrast and thermal conductivity ratio on the heat transfer results. Calculations have covered a wide range of the governing parameters, i.e., 0.01 {le} K{sub 1}/K{sub 2} {le} 100, 0.5 {le} k{sub 1}/k{sub 2} {le} 2 and 10 {le} Ra{sub 1} {le} 500. It is found that the normalized Nusselt number of a layered annulus with K{sub 1}/K{sub 2} 1. The feasibility of using an effective permeability (either based on a geometric mean or arithmetic mean) in the calculation of heat transfer results of a non-uniform system is also investigated. It is found that, for a Rayleigh number in the range between 10 and 1,000, the heat transfer prediction using a geometric average permeability usually gives a better result than that of using an arithmetic average. However, as the permeability contrast increases (i.e., K{sub 1}/K{sub 2} 1), calculationsmore » based on an effective permeability, either arithmetic average or geometric average, can not produce accurate results. The results obtained are useful for engineers in the design of insulation systems and nuclear waste repositories. Although each application may have a different emphasis (e.g., minimal heat loss for pipe insulation and least contamination for waste disposal), the present results suggest that, by a careful selection of the sublayer materials, most requirements can be met easily.« less