Onset of Darcy–Bénard convection using a thermal non-equilibrium model

• Published in: International journal of heat and mass transfer Vol. 45; no. 11; pp. 2221 - 2228
• Main Authors: Banu, Nurzahan, Rees, D.A.S.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2002; Elsevier
• Subjects: Asymptotic stability; Buoyancy-driven instability; Exact sciences and technology; Flows through porous media; Fluid dynamics; Fundamental areas of phenomenology (including applications); Heat transfer coefficients; Hydrodynamic stability; Mathematical models; Nonhomogeneous flows; Physics; Porous materials; Thermal effects; Convective instabilities; Porous medium flow; Darcy law; Non equilibrium conditions; Digital simulation; Horizontal layer; Modelling; Asymptotic solution; Benard convection; Heat transfer
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/S0017-9310(01)00331-3

In this paper we use a two-field model for the separate modelling of the solid and fluid phase temperature fields in a fluid-saturated porous medium, and, in particular, we consider how the onset criterion for convection in a horizontal layer is affected by the adoption of such a model. In general we find that both the critical Rayleigh number and wavenumber are modified by the presence of thermal non-equilibrium effects. It is shown that the well-known result of Lapwood [Proc. Cambridge Philos. Soc. 44 (1948) 508] which corresponds to local thermal equilibrium (LTE), is recovered when taking the thermal equilibrium limit of the non-equilibrium analysis. We also present asymptotic solutions for both small and large values of H the inter-phase heat transfer coefficient, H, and compare this with the numerical solutions. For intermediate values of H we find that the critical wavenumber is always larger than π, the critical value for the LTE case. In some cases this critical wavenumber may be very large compared with π.