On the hydrodynamics of salt-gradient solar ponds

SUMMARYThe concept of structural stability is discussed and brie y reviewed within the context of uid ow in porous media. Then the equations for non-Boussinesq (penetrative) convection in a porous medium with anisotropic permeability are analysed. It is shown, by deriving truly a priori estimates, that the solution exists in the natural functional framework and depends continuously on changes in the permeability. Since under appropriate circumstances the onset of thermal convection may be via Hopf bifurcation rather than stationary convection, such a priori continuous dependence estimates are of much value.

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“…This work has applications in the practical ÿeld of energy generation via a salt pond, cf. Rothmeyer [44], Tabor [45], and Zangrando [46].…”

Section: Structural Stabilitymentioning

confidence: 98%

Effect of anisotropic permeability on Darcy's law

Payne

Rodrigues

Straughan

2001

Math Methods in App Sciences

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“…We employ the non-dimensionalization of Chen and Chen [1] throughout. Thus, we use normal modes to represent the x and y dependence in (12), (10) , (13), and (11) , i.e., put…”

Section: Linearized Instabilitymentioning

confidence: 99%

Effect of property variation and modelling on convection in a fluid overlying a porous layer

Straughan

2001

Num Anal Meth Geomechanics

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SUMMARYAn accurate computational analysis is presented for the onset of thermal convection in a two-layer system which is comprised of a saturated layer of porous material described by Darcy's law, over which lies a layer of the same saturating #uid. The two-layer system is heated from below and the upper (#uid) surface is allowed to be "xed or stress free. The onset of convection may have a bi-modal nature in which convection may be dominated by the porous medium or by the #uid depending on the depths of the relative layers, but this is strongly controlled by material parameters. The e!ect of variation of relevant #uid and porous material properties is investigated in detail, as is the e!ect of the interface boundary condition between the #uid and the porous medium.

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“…Many analytical and numerical works have been published in the domain as well shedding an important insight into the thermal behaviours and the performance of a solar pond under various conditions. In particular, the effects due to several operating parameters such as the extracted heat load imposed on the pond, the boundaries heat losses, the pond depth as well as the thickness of the gradient zone have been thoroughly investigated [6][7][8][9][10][11]. Most of these studies were concerned, however, with the problem of one-dimensional heat diffusion with a constant salinity profile prescribed along the pond depth.…”

Section: Introductionmentioning

confidence: 99%