Power-Law Flow through a Packed Tube

Christopher, R. H.; Middleman, Stanley

doi:10.1021/i160016a011

Cited by 415 publications

(231 citation statements)

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“…After our two-scale expansions, it makes sense to link the effective shear rate (21)- (23) is not of Darcy law type and generally does not lead to the usual filtration law used in standard engineering treatment (e.g. as in [28], [81] and [68]):…”

Section: Remarkmentioning

confidence: 99%

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An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

Mikelić

2018

Lecture Notes in Mathematics

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Section: Remarkmentioning

confidence: 99%

“…Our laws, except for a tubular porous medium, are nonlocal and they cannot be reduced to a multi-dimensional variant of (28), connecting the Darcy velocity v and some power of ∇p. Most laboratory experiments are performed for onedimensional flows, which makes difficult observing any dimensional effect.…”

Section: Remarkmentioning

confidence: 99%

An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

Mikelić

2018

Lecture Notes in Mathematics

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“…A relatively simple way to describe non-Newtonian behavior is to express the apparent viscosity ( e  ) as a power function of shear rate y u   (e.g., Christopher and Middleman, 1965):…”

Section: Newtonian and Non-newtonian Fluidsmentioning

confidence: 99%

Unsaturated properties for non-Darcian water flow in clay

Liu

Birkhölzer

2012

Journal of Hydrology

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“…In equation (2) and (3) the permeability of the porous medium K for flows of non-Newtonian power-law fluids is given by the following relationships provided by Christopher and Middleman (1965) and Dharmadhikari and Kale (1985), respectively :…”

Section: Physical Model and Mathematical Analysismentioning

confidence: 99%

Solute Transport and Heat Transfer in Single-Phase Flow in Porous Medium With Generative/Destructive Chemical Reaction and Variable Viscosity Impacts

Achemlal¹,

Sriti²,

Elharoui³

et al. 2017

Frontiers in Heat and Mass Transfer

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In this paper we study the combined free convection, due to thermal and species diffusion, of a viscous incompressible non Newtonian fluid over a vertical plate embedded in a saturated porous medium with three thermal states of the surface and a constant concentration in the presence of a chemical reaction. The effect of temperature dependent viscosity is also investigated. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a unique similarity transformation and the resulting coupled differential equations are then solved numerically by a computational program based on the fifth order Runge-Kutta scheme with shooting iteration technique. The results are illustrated and the physical aspect is discussed for temperature and concentration profiles, as well as the Nusselt and Sherwood numbers for various values of the parameters, which govern the problem.

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Power-Law Flow through a Packed Tube

Cited by 415 publications

References 1 publication

An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

Unsaturated properties for non-Darcian water flow in clay

Solute Transport and Heat Transfer in Single-Phase Flow in Porous Medium With Generative/Destructive Chemical Reaction and Variable Viscosity Impacts

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