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.
Funder
Università degli Studi di Napoli Federico II
Publisher
Springer Science and Business Media LLC
Subject
General Chemical Engineering,Catalysis
Cited by
1 articles.
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