We have investigated the onset of convection instability in a heterogeneous inclined porous layer. Our equations also account for local thermal non-equilibrium. We modelled the effect of heterogeneity by assuming that the layer is composed of two porous sub-layers with different properties, such as permeability, fluid conductivity, solid conductivity, interphase heat transfer coefficient and porosity. We identified which of these factors have major and which have minor effect on the instability. We also characterized the accuracy of one-term Galerkin approximation for this problem. In order to do this, we compared the results obtained by Galerkin approximation with the results obtained by a highly accurate numerical solver.
Sloping layer Local thermal non-equilibrium Porous medium Instability Natural convection
This is a preview of subscription content, log in to check access.
A.V.K. gratefully acknowledges the support of the Alexander von Humboldt Foundation through the Humboldt Research Award.
Banu, N., Rees, D.A.S.: Onset of Darcy–Bénard convection using a thermal non-equilibrium model. Int. J. Heat Mass Transf. 45, 2221–2228 (2002)CrossRefGoogle Scholar
Barletta, A., Storesletten, L.: Thermoconvective instabilities in an inclined porous channel heated from below. Int. J. Heat Mass Transf. 54, 2724–2733 (2011)CrossRefGoogle Scholar
Caltagirone, J.P., Bories, S.: Solutions and stability criteria of natural convective flow in an inclined porous layer. J. Fluid Mech. 155, 267–287 (1985)CrossRefGoogle Scholar
McKibbin, R.: Convective instability in layered sloping warm-water aquifers. Eur. J. Mech. B 47, 68–79 (2014)CrossRefGoogle Scholar
Nield, D.A.: Effects of local thermal nonequilibrium in steady convective processes in a saturated porous medium: forced convection in a channel. J. Porous Media 1, 181–186 (1998)Google Scholar
Nield, D.A.: A note on local thermal non-equilibrium in porous media near boundaries and interfaces. Transp. Porous Media 95, 581–584 (2012)CrossRefGoogle Scholar