Effects of Anisotropy on Convective Flow Through Porous Media

Storesletten, L.

doi:10.1016/b978-008042843-7/50011-8

Cited by 51 publications

(33 citation statements)

References 33 publications

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“…The in£uence of anisotropic permeability on the £ow pattern for the oceanic crust was studied by Rosenberg et al [39]. The reader is referred to Storesletten [46] for a review on convection in anisotropic media.…”

Section: Anisotropic Permeability and Mechanical Dispersionmentioning

confidence: 99%

Chaotic thermohaline convection in low-porosity hydrothermal systems

Schoofs

Spera

Hansen

1999

Earth and Planetary Science Letters

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Fluids circulate through the Earth's crust perhaps down to depths as great as 5^15 km, based on oxygen isotope systematics of exhumed metamorphic terrains, geothermal fields, mesozonal batholithic rocks and analysis of obducted ophiolites. Hydrothermal flows are driven by both thermal and chemical buoyancy; the former in response to the geothermal gradient and the latter due to differences in salinity that appear to be ubiquitous. Topographically driven flows generally become less important with increasing depth. Unlike heat, solute cannot diffuse through solid matrix. As a result, temperature perturbations advect more slowly than salinity fluctuations by the factor P, but diffuse more rapidly by the factor U/D and are so smoothed out more efficiently. Here, P is porosity, while U and D denote the thermal and chemical molecular diffusivity, respectively. Double-advective instabilities may play a significant role in solute and heat transport in the deep crust where porosities are low. We have studied the stability and dynamics of the flow as a function of P and thermal and chemical buoyancy, for situations where mechanical dispersion of solute dominates over molecular diffusion in the fluid. In the numerical experiments, a porous medium is heated from below while solute provides a stabilizing influence. For typical geological parameters, the thermohaline flow appears intrinsically chaotic. We attribute the chaotic dynamical behavior of the flow to a dominance of advective and dispersive chemical transfer over the more moderate convective heat transfer, the latter actually driving the flow. Fast upward advective transport and lateral mixing of solute leads to formation of horizontal chemical barriers at depth. These gravitationally stable interfaces divide the domain in several layers of distinct composition and lead to significantly reduced heat flow for thousands of years. The unsteady behavior of thermochemical flow in low-porosity regions has implications for heat transport at mid-ocean ridges, for ore genesis, for metasomatism and metamorphic petrology, and the diagenetic history of sediments in subsiding basins. ß 1999 Elsevier Science B.V. All rights reserved.

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Section: Anisotropic Permeability and Mechanical Dispersionmentioning

confidence: 99%

Chaotic thermohaline convection in low-porosity hydrothermal systems

Schoofs

Spera

Hansen

1999

Earth and Planetary Science Letters

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“…Equation 3.9 coincides with that of Storesletten (1998) for the case of single component fluid-saturated anisotropic porous layer. For an isotropic porous medium, ξ = 1 the Eq.…”

Section: Stationary Statementioning

confidence: 52%

“…The Darcy model with time derivative is employed for the momentum equation and the both the cross-diffusion terms are included in the temperature and concentration equations. With these assumptions, the basic governing equations are given in the following section (Storesletten 1998;Mojtabi and Charrier-Mojtabi 2005;Nield and Bejan 2006) (Fig. 1).…”

Section: Mathematical Formulationmentioning

confidence: 99%

Linear and Non-linear Double Diffusive Convection in a Fluid-Saturated Anisotropic Porous Layer with Cross-Diffusion Effects

2009

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The double diffusive convection in a horizontal anisotropic porous layer saturated with a Boussinesq binary fluid, which is heated and salted from below in the presence of Soret and DuFour effects is studied analytically using both linear and non-linear stability analyses. The linear analysis is based on the usual normal mode technique, while the non-linear analysis is based on a minimal representation of double Fourier series. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number, wavenumbers for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effects of anisotropy parameter, solute Rayleigh number, and Soret and DuFour parameters on the stationary, oscillatory convection, and heat and mass transfer are shown graphically. Some known results are recovered as special cases of the present problem.

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“…The effects of anisotropy and surface boundary conditions on convection in a horizontal porous layer were studied by McKibbin [14]. A very good collection of references on the topic on the effects of anisotropy on convective flow through porous media can be found in the review paper by Storesletten [9]. Further, Degan et al [15], Zhang et al [16], Bera et al [17], Bera and Khalili [18], and Kumar and Bera [19] have studied the convective heat transfer in a vertical anisotropic porous layer and in a cavity filled with an anisotropic porous medium.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the performed studies have usually been concerned with homogeneous isotropic porous structures. However, in many practical situations the porous materials are anisotropic in their mechanical and thermal properties [9]. An example of such a medium is loft insulation which usually has lower permeability across the insulating layer than it has in the perpendicular directions.…”

Section: Introductionmentioning

confidence: 99%

Forced convection heat transfer inside an anisotropic porous channel with oblique principal axes: Effect of viscous dissipation

Mobedi

Cekmer

Pop

2010

International Journal of Thermal Sciences

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a b s t r a c tAn analytical study on laminar and fully developed forced convection heat transfer in a parallel-plate horizontal channel filled with an anisotropic permeability porous medium is performed. The principal axis of the anisotropic porous medium is oriented from 0 to 90 degrees. A constant heat flux is applied on the outer wall of the channel. Both clear (Newtonian) fluid and Darcy viscous dissipations are considered in the energy equation. Directional permeability ratio parameter A * is defined to combine both the effect of the dimensionless permeability ratio parameter K * ¼(K 1 /K 2 ) and orientation angle 4 into one parameter.The effects of the parameter A * , the Darcy number Da and the modified Brinkman number Br * on the heat transfer and fluid flow characteristics in the channels are investigated and presented in graphs. The obtained results show that the parameters A * , Da and Br * have strong effects on the dimensionless normalized velocity and temperature profiles as well as on the Nusselt number. It is found that for a particular value of A * , called as critical value A cr * , the external heat applied to the surface of the channel is balanced by the internal heat generation due to viscous dissipation and the bulk mean temperature approaches the wall temperature. Hence, the Nusselt number approaches infinity for the critical values A cr * .

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Effects of Anisotropy on Convective Flow Through Porous Media

Cited by 51 publications

References 33 publications

Chaotic thermohaline convection in low-porosity hydrothermal systems

Chaotic thermohaline convection in low-porosity hydrothermal systems

Linear and Non-linear Double Diffusive Convection in a Fluid-Saturated Anisotropic Porous Layer with Cross-Diffusion Effects

Forced convection heat transfer inside an anisotropic porous channel with oblique principal axes: Effect of viscous dissipation

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