TY - JOUR
TI - A theoretical and numerical study of thermosolutal convection: stability of a salinity gradient solar pond
AU - Akrour Dalila
AU - Tribeche Mouloud
AU - Kalache Djamel
JN - Thermal Science
PY - 2011
VL - 15
IS - 1
SP - 67
EP - 80
PT - Article
AB - 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, µa = 0.8, and f = 0.5.