Onset of Natural Convection in a Horizontal Porous Medium With Mixed Thermal Boundary Conditions

Abstract

The mathematical formalism developed by Nield (1968) has been used to calculate critical Rayleigh numbers and critical wavenumbers for the onset of natural convection in a horizontal porous medium subject to mixed thermal boundary conditions. Two practically important cases were examined. The first case corresponds to impermeable top and bottom boundaries, and the second corresponds to an impermeable bottom boundary and an open top boundary. It was found that at limiting Biot numbers of 0 and {infinity}, the calculated critical Rayleigh numbers and critical wavenumbers agreed very well with those given in the literature. Numerical values are given for a wide range of intermediate Biot numbers. The results of these analyses were applied to analysis of experimental data, on the thermal performance of low-density loose-till fiberglass insulation tested in a simulated attic with an open top boundary. Experimental critical Rayleigh numbers were substantially lower than the ideal value of 27.1. The mixed thermal boundary conditions were not sufficient to explain the difference between the experimental critical Rayleigh numbers and the ideal value. 8 refs., 4 figs., 3 tabs.