Abstract
Thermogravitational separation has until now, been used in different heated vertical cells called thermogravitational columns. The cell can be an annular cavity with two isothermal faces maintained at different temperatures. The main objective of this paper is to study the two dimensional coupled convection with thermodiffusion process. It concerns a theoretical and numerical investigation of species separation in a binary liquid mixture saturating a horizontal porous annulus space where the inner cylinder is heated isothermally. This kind of geometry is used instead of the annular vertical cell, hence the novelty of this technique. Analytical resolution is performed using the perturbation method function of time versus the corresponding physics (Raleigh and Lewis numbers...). Results reveal that the separation can be increased with an optimum for small values of Rayleigh number. Further, these values are less important than the critical value of Raleigh leading to the loss of unicellular flow stability found in literature.
Highlights
Thermogravitational diffusion is the combination of two phenomena; convection and thermodiffusion
We propose a new procedure coupling the convection and the thermodiffusion to obtain an important separation between the top and the bottom of the annular horizontal porous layer
Of the coupled mass, energy and momentum equations (Eqs. (8) to (10)) using the perturbation method is conducted
Summary
Thermogravitational diffusion is the combination of two phenomena; convection and thermodiffusion. Coupling these two phenomena leads to species separation constituting a mixture of gas or liquid unfilled a welldefined geometrical space. Thermal diffusivity of the mixture a∗ = λ∗/(ρc)f Mass fraction of the denser component of the mixture Mass diffusion coefficient (m2.s−1) Thermodiffusion coefficient (m2.s−1.K−1) Dimensional gap width e = re − ri (m) Gravitational acceleration (m.s2). Wave number Permeability of the porous medium (m2) Lewis number Le = a∗/D∗. Radius ratio R = re/ri Thermal filtration Rayleigh number Ra = gβ (Ti − Te) (ρc)f K ri/λ∗ν Critical Rayleigh number Separation. Dimensionless time Velocity field (m.s−1) Velocity components (m.s−1). Greek symbol Thermal expansion coefficient (K−1) Solutal expansion coefficient (m3.kg1)
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