Local thermal non-equilibrium effects in the Darcy–Bénard instability with isoflux boundary conditions

• Published in: International journal of heat and mass transfer Vol. 55; no. 1; pp. 384 - 394
• Main Authors: Barletta, A., Rees, D.A.S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 15.01.2012; Elsevier
• Subjects: Boundary conditions; Buoyancy-driven instability; Buoyancy-induced instability; Constant heat flux; Darcy–Bénard problem; Exact sciences and technology; Flows through porous media; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); Heat flux; Heat transfer; Hydrodynamic stability; Instability; Local thermal non-equilibrium; Mathematical models; Nonhomogeneous flows; Physics; Porous medium; Stability; Wavelengths; Local thermal non-equilibrium; Constant heat flux; Porous medium; Darcy–Bénard problem; Buoyancy-induced instability; Convective instabilities; Porous medium flow; Darcy law; Digital simulation; Boundary conditions; Horizontal layer; Modelling; Benard convection; Thermal equilibrium
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2011.09.031

The Darcy–Bénard problem with constant heat flux boundary conditions is studied in a regime where the fluid and solid phases are in local thermal non-equilibrium. The onset conditions for convective instability in the plane porous layer are investigated using a linear stability analysis. Constant heat flux boundary conditions are formulated according to the Amiri–Vafai–Kuzay Model A, where the boundary walls are assumed as impermeable and with a high thermal conductance. The normal mode analysis of the perturbations imposed on the basic state leads to a one-dimensional eigenvalue problem, solved numerically to determine the neutral stability condition. Analytical solutions are found for the limit of small wave numbers, and in the regime where the conductivity of the solid phase is much larger than the conductivity of the fluid phase. A comparison with the corresponding results under conditions of local thermal equilibrium is carried out. The critical conditions for the onset of convection correspond to a zero wave number only when the inter-phase heat transfer coefficient is sufficiently large. Otherwise, the critical conditions correspond to a nonzero wave number.