Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model

The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Brinkman model is employed. Three cases of free–free, rigid–r...

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Bibliographic Details
Published in:Transport in porous media 2010-02, Vol.81 (3), p.409-422
Main Authors: Kuznetsov, A. V., Nield, D. A.
Format: Article
Language:English
Subjects:
Brinkman model
Brownian motion
Buoyancy
Civil Engineering
Classical and Continuum Physics
Conservation
Earth and Environmental Science
Earth Sciences
Earth, ocean, space
Energy conservation
Engineering and environment geology. Geothermics
Exact sciences and technology
Free boundaries
Geotechnical Engineering & Applied Earth Sciences
Hydrocarbons
Hydrogeology
Hydrology. Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Mathematical analysis
Nanocomposites
Nanofluids
Nanomaterials
Nanoparticles
Nanostructure
Pollution, environment geology
Porous media
Sedimentary rocks
Thermal energy
Thermal instability
Thermophoresis
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Summary:The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Brinkman model is employed. Three cases of free–free, rigid–rigid, and rigid–free boundaries are considered. The analysis reveals that for a typical nanofluid (with large Lewis number), the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles, whereas the contribution of nanoparticles to the thermal energy equation is a second-order effect. It is found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of the nanoparticles. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution.
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-009-9413-2