Compressible gas in porous media: a finite amplitude analysis of natural convection

• Published in: International journal of heat and mass transfer 1997, Vol.40 (7), p.1585-1589
• Main Authors: Stauffer, P.H., Auer, L.H., Rosenberg, N.D.
• Format: Article
• Language: English
• Subjects: Convection and heat transfer; Exact sciences and technology; Flows through porous media; Fluid dynamics; Fundamental areas of phenomenology (including applications); Nonhomogeneous flows; Physics; Turbulent flows, convection, and heat transfer
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/S0017-9310(96)00222-0

The theory of thermally driven convection of dry air in a porous medium is reviewed. The critical Rayleigh number for air is the same as for liquid, 4Π 2, but the thermal gradient used is decreased by the adiabatic gradient of air. Because of the differences in the physical properties of air and water, initiation of convection requires the product of gradient and permeability to be thousands of times greater for air than for water. Finite amplitude analysis of the problem for Ra< 300 shows that: (1) the code predicts the onset of convection in an air filled porous medium; (2) at low thermal gradient, Ra vs Nu curves are nearly the same for air and water; (3) the slope of the Ra vs Nu curve matches well with experimental data reported by others for water; (4) time to steady state decreases approximately as the square root of Nusselt number.