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RESEARCH PAPERS

# A Linear Stability Study of the Gradient Zone of a Solar Pond

[+] Author and Article Information
L. Kaffel Rebaï

Unité de Recherche en Mécanique et Energétique, Ecole Nationale d’Ingénieurs de Tunis, 2000 Tunis, Tunisia and IMFT, UMR 5502 CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, Franceleila.kaffel@enit.rnu.tn

A. K. Mojtabi

IMFT, UMR 5502 CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France

M. J. Safi

Unité de Recherche en Mécanique et Energétique, Ecole Nationale d’Ingénieurs de Tunis, 2000 Tunis, Tunisia

A. A. Mohamad

Department of Mechanical and Manufacturing Engineering, The University of Calgary, Calgary, AB, T2N 1N4, Canada

J. Sol. Energy Eng 128(3), 383-393 (Nov 07, 2005) (11 pages) doi:10.1115/1.2210498 History: Received March 31, 2005; Revised November 07, 2005

## Abstract

The linear stability of a plane layer with horizontal temperature and concentration stratification corresponding to gradient zone of a solar pond is investigated. The problem is described by Navier-Stokes equations with Boussinesq-Oberbeck approximation. Two source terms are introduced in the energy equations: the absorption of solar energy characterized by the extinction radiative coefficient $μe$ and by the parameter $f$ defined as the ratio of extracted heat flux to absorbed heat flux in the lower convective zone. The influence of the parameters $μe$ and $f$ on the onset of thermosolutal convection in the case of confined and infinite layers is analyzed. It is found that convection starts in an oscillatory state, independently of the $RaS$ value. Different convection solutions were found for marginal stability and steady state.

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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 1

General structure of a solar pond

Figure 2

Critical Rayleigh number as a function of solute Rayleigh number in the gradient zone of an infinite extension solar pond for different values of μe and f (Pr=7, Le=100, N=5): (a) μe=0.8 and (b) μe=0.2

Figure 3

Wave number as a function of solute Rayleigh number in the gradient zone of an infinite extension solar pond for different values of μe and f (Pr=7, Le=100, N=5): (a) μe=0.8 and (b) μe=0.2

Figure 4

Critical Rayleigh number of oscillatory state as a function of solutal Rayleigh number in the gradient zone of an infinite extension solar pond for different values of μe and f (Pr=7, Le=100, N=M=2)

Figure 5

Hopf frequency and wave number as functions of solutal Rayleigh number in the gradient zone of an infinite extension of a solar pond for different values of μe and f (Pr=7, Le=100, N=M=2): (a) Hopf frequency and (b) wave number as a function of solutal Rayleigh number

Figure 6

Critical Rayleigh number of the steady state as a function of solutal Rayleigh number in the gradient zone of a finite extension solar pond for different values of μe and f (A=1, Pr=7, Le=100, N=2, M=3).

Figure 7

Critical Rayleigh number and the Hopf frequency of the oscillatory state as functions of solutal Rayleigh number in the gradient zone of a finite extension solar pond for different values of μe and f (Pr=7, Le=100, N=M=2): (a) critical Rayleigh number and (b) Hopf frequency

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