Nonlinear thermal convection in anisotropic porous media

Kvernvold, Oddmund; Tyvand, Peder A.

doi:10.1017/s0022112079002445

Cited by 146 publications

(65 citation statements)

References 12 publications

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“…1) indicate the material properties that are parallel and perpendicular to the temperature gradient; K k and k k are used in equation (1) in place of the average values (Straus 1974;Straus and Schubert 1978;Kvernvold and Tyvand 1979). A grass canopy may be modeled as a series of upright cylindrical rods (grass blades) of radius a that are spaced a distance 2b apart, as shown in figure 1.…”

Section: Thermal-convection Hypothesismentioning

confidence: 99%

A Porous Convection Model for Grass Patterns

Thompson

Daniels

2010

The American Naturalist

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Spatial ecological patterns are usually ascribed to Turingtype reaction-diffusion or scale-dependent feedback processes, but morphologically indistinguishable patterns can be produced by instabilities in fluid flow. We present a new hypothesis that suggests that fluid convection and chill damage to plants could form vegetation patterns with wavelengths ≈1-2 times the plant height. Previous hypotheses for small-scale vegetation pattern formation relied on a Turing process driven by competition for water, which is thought to occur in large vegetation patterns. Predictions of the new hypothesis were consistent with properties of natural grass patterns in North Carolina, contradicting the Turing hypothesis. These results indicate that similarities in pattern morphology should not be interpreted as implying similarities in the pattern-forming processes, that small-wavelength vegetation patterns may arise from mechanisms that are distinct from those generating long-wavelength vegetation patterns, and that fluid instabilities should be recognized as a cause of ecological patterns.

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Section: Thermal-convection Hypothesismentioning

confidence: 99%

A Porous Convection Model for Grass Patterns

Thompson

Daniels

2010

The American Naturalist

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“…The first study in this area was given by Castinel and Combarnous [28], who obtained the criterion for the onset of convection in a layer with anisotropic permeability and impermeable upper and lower boundaries. Epherre [29] applied anisotropy in both permeability and thermal conductivity, Kvernvold and Tyvand [30] studied the steady finite amplitude convection and derived criterion for the onset of convection. Tyvand [31] studied the onset of thermohaline convection in anisotropic porous media, while anisotropy in only thermal conductivity has been studied by Storesletten [32].…”

mentioning

confidence: 99%

Effect of Internal Heating on Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Medium

Srivastava¹,

Bhadauria²,

Hashim³

2014

AMSA

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Abstract-The effect of internal heat source on double diffusive convection in a couple stress fluid saturated horizontal anisotropic porous layer was studied analytically by performing linear and nonlinear stability analyses. For linear stability analysis, normal mode technique was used, whereas for nonlinear stability analysis a minimal representation of Fourier series upto two terms was used. Effects of anisotropic parameter, couple stress parameter, solute Rayleigh number, Vadász number, Lewis number, internal heat source parameter on stationary, oscillatory and finite amplitude convection were obtained and shown graphically. Also the graphs for heat and mass transport, streamlines, isotherms, isohalines for steady and unsteady cases were drawn. It was found that internal heat source parameter had destabilizing effect on all modes of convection. Heat transport increased and mass transport decreased with the increase in internal heat source parameter.

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“…Their results were extended by Epherre (1975) [8] and Kvernvold and Tyvand (1979) [9] who considered a more general type of anisotropy. Convection attributable to side-heating in a vertical layer has been considered by several authors.…”

Section: Introductionmentioning

confidence: 79%

Hydrodynamic Anisotropy Effects on Radiation-Mixed Convection Interaction in a Vertical Porous Channel

Degan¹,

Akowanou²,

Fagbemi³

et al. 2016

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The effects of hydrodynamic anisotropy on the mixed-convection in a vertical porous channel heated on its plates with a thermal radiation are investigated analytically for fully developed flow regime. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity. The generalized Brinkman-extended Darcy model which allows the no-slip boundary-condition on solid wall is used in the formulation of the problem. The flow reversal, the thermal radiation influence for natural, and forced convection are considered in the limiting cases for low and high porosity media. It was found that the anisotropic permeability ratio, the orientation angle of the principal axes of permeability and the radiation parameter affected significantly the flow regime and the heat transfer.

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Nonlinear thermal convection in anisotropic porous media

Cited by 146 publications

References 12 publications

A Porous Convection Model for Grass Patterns

A Porous Convection Model for Grass Patterns

Effect of Internal Heating on Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Medium

Hydrodynamic Anisotropy Effects on Radiation-Mixed Convection Interaction in a Vertical Porous Channel

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