Variable viscosity effects on the onset of convection in porous media

Kassoy, D. R.; Zebib, Abdelfattah

doi:10.1063/1.861083

Cited by 79 publications

(38 citation statements)

References 4 publications

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“…Then R 24 to 240 if the bulk permeability of the convecting medium is 4 to 40 millidarcys. Because of the large thermal-expansion coefficient (Straus and Schubert, 1977) and the temperature-dependent viscosity of water (Kassoy and Zebib, 1975), R c for the ocean crust is less than 10, whether the top of the cell is permeable or impermeable (Ribando et al, 1976). Therefore, convection in the basement is indicated strongly.…”

Section: Discussionmentioning

confidence: 99%

Permeability, Underpressures, and Convection in the Oceanic Crust at Deep Sea Drilling Project Hole 504B

Zoback¹,

Anderson²

1983

Initial Reports of the Deep Sea Drilling Project

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In order to study the variation in physical parameters responsible for the transition from convective to conductive heat flow near mid-ocean ridges, in situ permeability and pore-pressure measurements were made 200 meters into oceanic crustal Layer 2A in DSDP Hole 504B, on the south flank of the Costa Rica Rift. Conventional "slug" and constant-rate injection tests were made below a hydraulic packer set at various depths in the hole. The packer was first set in a massive flow unit 37 meters below the sediment/basement interface. The bulk permeability of the 172.5 meters of pillow basalts and basaltic flows below the packer was found to be about 40 millidarcys (4 × 10~1 0 cm 2 ). Measurements over 3-and 15-meter intervals at the bottom of the hole in an altered pillow zone indicated a bulk permeability of 2 to 4 millidarcys and formation pore pressures approximately 10 bars (~2%) below hydrostatic. Interpretation of the data with respect to simple numerical convection models suggests that the transition from convective to conductive heat flow is controlled by the cessation of convective heat transport through the sedimentary layer, rather than the cessation of convection in the basement. Furthermore, the agreement between observed and modelled underpressures implies that Hole 504B penetrated an active ocean crustal convection system. The thick sedimentary layer, layers of basal chert, and massive flow basalts above the Layer 2A pillow flows apparently form an impermeable lid, effectively isolating the convective system from the ocean.

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Section: Discussionmentioning

confidence: 99%

Permeability, Underpressures, and Convection in the Oceanic Crust at Deep Sea Drilling Project Hole 504B

Zoback¹,

Anderson²

1983

Initial Reports of the Deep Sea Drilling Project

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“…On the other hand, in a notable study, commenting on [25][26][27], Nield [30,31] argued that the effect of property variation on free convection is artificial and should disappear if one uses an effective Rayleigh number based on mean values. Nield [31] showed that, if the mean values are used, the critical Rayleigh number remains unaltered, which indicates that the flow of a fluid with temperature-dependent viscosity is no less stable than a constant-property one.…”

Section: Nusselt Number Bénard Problemmentioning

confidence: 99%

“…fluid flow patterns compared to constant property solutions [24]. Some authors (see for example [25][26][27][28]) have investigated natural convection with temperature dependent viscosity while keeping the other fluid properties constant (this assumption is known to be valid for some fluids [29]). …”

Section: Nusselt Number Bénard Problemmentioning

confidence: 99%

Effects of temperature-dependent viscosity on Bénard convection in a porous medium using a non-Darcy model

Hooman

Gurgenci

2008

International Journal of Heat and Mass Transfer

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Temperature dependent viscosity variation effect on Bénard convection, of a gas or a liquid, in an enclosure filled with a porous medium is studied numerically, based on the general model of momentum transfer in a porous medium. The Arrhenius model, which proposes an exponential form of viscosity-temperature relation, is applied to examine three cases of viscosity-temperature relation: constant (µ=µ C ), decreasing (down to 0.13µ C ) and increasing (up to 7.39µ C ). Effects of fluid viscosity variation on isotherms, streamlines, and the Nusselt number are studied. Application of the effective and average Rayleigh number is examined. Defining a reference temperature, which does not change with the Rayleigh number but increases with the Darcy number, is found to be a viable option to account for temperature-dependent viscosity variation.

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“…The fundamental analysis of convection through porous media with temperature dependent viscosity is driven by several contemporary engineering applications from the cooling of electronic devices to porous journal bearings and is important for studying the variations in constitutive properties. The effect of variable viscosity for convective heat transfer through porous media has also been widely studied (e.g., [13][14][15][16][17][18][19]). The effect of variations in viscosity on the instability of flow and temperature fields are discussed by Kassoy and Zebib [13] and Gray et al [14].…”

Section: Introductionmentioning

confidence: 99%

“…The effect of variable viscosity for convective heat transfer through porous media has also been widely studied (e.g., [13][14][15][16][17][18][19]). The effect of variations in viscosity on the instability of flow and temperature fields are discussed by Kassoy and Zebib [13] and Gray et al [14]. Lai and Kulacki [15] considered the variable viscosity effect for mixed convection along a vertical plate embedded in a saturated porous medium.…”

Section: Introductionmentioning

confidence: 99%

Effect of variable viscosity on vortex instability of non-Darcy free convection boundary layer flow adjacent to a non-isothermal horizontal surface in a porous medium

2012

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In this article, we study the effect of variable viscosity on the flow and vortex instability of non-Darcian free convection boundary layer flow on a horizontal surface in a saturated porous medium. The wall temperature is a power function of the distance from the origin. The variation of viscosity is expressed as an exponential function of temperature. The transformed boundary layer equations, which are developed using a non similar solution approach, are solved by means of a finite difference method. The analysis of the disturbance flow is based on linear stability theory. The local Nusselt number, critical Rayleigh number and the associated wave number at the onset of vortex instability are presented over a wide range of wall to ambient viscosity ratio parameters μ*= μ w /μ ∞ . The variable viscosity effect is found to enhance the heat transfer rate and destabilize the flow for liquid heating, while the opposite trend is true for gas heating.

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Variable viscosity effects on the onset of convection in porous media

Cited by 79 publications

References 4 publications

Permeability, Underpressures, and Convection in the Oceanic Crust at Deep Sea Drilling Project Hole 504B

Permeability, Underpressures, and Convection in the Oceanic Crust at Deep Sea Drilling Project Hole 504B

Effects of temperature-dependent viscosity on Bénard convection in a porous medium using a non-Darcy model

Effect of variable viscosity on vortex instability of non-Darcy free convection boundary layer flow adjacent to a non-isothermal horizontal surface in a porous medium

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