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Compressibility effect on Darcy porous convection
- Publication Year :
- 2022
-
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 variation. In this paper the linear analysis of the Darcy-B\'enard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor $\beta$ 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 thermodynamic consistent instability results. Via linear instability analysis of the conduction solution, the critical Rayleigh-Darcy number for the onset of convection is determined as a function of a dimensionless parameter $\widehat{\beta}$ proportional to the compressibility factor $\beta$, proving that $\widehat{\beta}$ enhances the onset of convective motions.
- Subjects :
- Physics - Fluid Dynamics
Mathematical Physics
76E06, 76E07, 76Exx, 76S05, 76Sxx
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2210.08075
- Document Type :
- Working Paper