Open AccessA theoretical and numerical study of thermosolutal convection: stability of a salinity gradient solar pond
Author(s) -
Dalila Akrour,
Mouloud Tribeche,
Djamel Kalache
Publication year - 2011
Publication title -
thermal science/thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci1101067a
Subject(s) - temperature gradient , convection , rayleigh number , mechanics , perturbation (astronomy) , boundary value problem , thermodynamics , galerkin method , stability (learning theory) , temperature salinity diagrams , infinitesimal , thermophoresis , maple , physics , salinity , thermal , mathematics , natural convection , mathematical analysis , meteorology , geology , computer science , nanofluid , quantum mechanics , machine learning , finite element method , oceanography , biology , botany
A theoretical and numerical study of the effect of thermodiffusion on the stability of a gradient layer is presented. It intends to clarify the mechanisms of fluid dynamics and the processes which occur in a salinity gradient solar pond. A mathematical modelling is developed to describe the thermodiffusion contribution on the solar pond where thermal, radiative, and massive fluxes are coupled in the double diffusion. More realistic boundary conditions for temperature and concentration profiles are used. Our results are compared with those obtained experimentally by authors without extracting the heat flux from the storage zone. We have considered the stability analysis of the equilibrium solution. We assumed that the perturbation of quantities such as velocity, temperature, and concentration are infinitesimal. Linearized equations satisfying appropriate prescribed boundary conditions are then obtained and expanded into polynomials form. The Galerkin method along with a symbolic algebra code (Maple) are used to solve these equations. The effect of the separation coefficient y is analyzed in the positive and negative case. We have also numerically compared the critical Rayleigh numbers for the onset of convection with those obtained by the linear stability analysis for Le = 100, ?a = 0.8, and f = 0.5.