Numerical and Analytical Studies of Soret-Driven Convection Flow Inside an Annular Horizontal Porous Cavity

• Published in: Fluids (Basel) Vol. 6; no. 10; p. 357
• Main Authors: Mojtabi, Abdelkader, Sioud, Khairi, Bergeon, Alain, Charrier-Mojtabi, Marie Catherine
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.10.2021; MDPI
• Subjects: Agreements; Approximation; Binary fluids; Boundary conditions; Concentric cylinders; Configurations; Convection; Exact solutions; Fluid mechanics; Free convection; Galerkin method; Mathematical analysis; Mechanics; Parallel flow; Perturbation methods; Physics; porous medium; Rayleigh number; Separation; separation of binary fluid; Software; Soret-driven convection; spectral method; Stability analysis; Temperature gradients; Thickness; Separation of binary fluid; Spectral method; Soret-driven convection separation of binary fluid porous medium spectral method; Soret-driven convection; Porous medium
• ISSN: 2311-5521; 2311-5521
• DOI: 10.3390/fluids6100357

This paper studies the species separation of a binary fluid in a porous cavity between two horizontal concentric cylinders, submitted to a temperature gradient. The thickness of the cavity is e=Ro−Ri, where Ri and Ro are the internal and external radius, respectively. The numerous previous experiments performed in thermogravitational vertical columns (TGCs) showed that in order to obtain a significant separation, the thickness of the cell must be very small, compared with its height. Therefore, in our configuration, we considered e≪Ri. The solution is assumed to be axisymmetric. Under the assumptions of parallel flow and forgotten effect, an analytical solution is obtained using Maple software, and the results are compared with those found numerically using Comsol Multiphysics. In natural convection, our results are in very good agreement with those evaluated with a regular perturbation method in powers of the dimensionless gap width ε=eRi  of order 15, and with the Galerkin method. The species separation calculated for our configuration is very close to the one obtained in a TGC column of height: H=πRi. One of the main interests of the analytical solution presented here is that it can be used as a basic solution for a stability study analysis.