Compressibility Effect on Darcy Porous Convection

Abstract

Abstract Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variations. In this paper, the linear analysis of the Darcy-Bénard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor $$\beta$$ β which describes the compressibility of the fluid and plays an essential role in the instability results. In particular, in the Oberbeck-Boussinesq approximation, a more realistic constitutive equation for the fluid density is employed in order to obtain more thermodynamically consistent instability results. The critical Rayleigh-Darcy number for the onset of convection is determined, via linear instability analysis of the conduction solution, as a function of a dimensionless parameter $$\widehat{\beta }$$ β ^ proportional to the compressibility factor $$\beta$$ β , proving that $$\widehat{\beta }$$ β ^ enhances the onset of convective motions. Article Highlights The onset of convection in fluid-saturated porous media is analyzed, taking into account fluid compressibility effect. The critical Rayleigh-Darcy number is determined in a closed algebraic form via linear instability analysis. The critical Rayleigh-Darcy number is shown to be a decreasing function of the dimensionless compressibility factor.