A determination of the effective viscosity for the Brinkman–Forchheimer flow model

Givler, Richard C.; Altobelli, Stephen A.

doi:10.1017/s0022112094003368

Cited by 283 publications

(132 citation statements)

References 12 publications

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“…It has previously been shown [43] that setting  eff =  f results in acceptable outcomes. The same assumption is, therefore, made throughout this study.…”

Section: Boundary Conditionsmentioning

confidence: 99%

On the effects of exothermicity and endothermicity upon the temperature fields in a partially-filled porous channel

Karimi

Agbo

Khan

et al. 2015

International Journal of Thermal Sciences

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. (2015) On the effects of exothermicity and endothermicity upon the temperature fields in a partially-filled porous channel. International Journal of Thermal Sciences. Copyright © 2015 ElsevierA copy can be downloaded for personal non-commercial research or study, without prior permission or charge Content must not be changed in any way or reproduced in any format or medium without the formal permission of the copyright holder assumption and, therefore, the validity of the LTE is examined. This is done for a wide range of pertinent parameters including Biot number, conductivity ratio, Darcy number and thickness of the porous insert. It is found that the thermal behaviour of the investigated partially filled system is influenced by the heat sources in both solid and fluid phase. It is further shown that the LTE approach remains an acceptable assumption only for some specific regions of the parametric space. Furthermore, the occurrence of temperature gradient bifurcation on the surface of the porous-fluid interface is examined.It is demonstrated that this effect is highly sensitive to the intensity of the energy sources.

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“…It has previously been shown [43] that setting  eff =  f results in acceptable outcomes. The same assumption is, therefore, made throughout this study.…”

Section: Boundary Conditionsmentioning

confidence: 99%

On the effects of exothermicity and endothermicity upon the temperature fields in a partially-filled porous channel

Karimi

Agbo

Khan

et al. 2015

International Journal of Thermal Sciences

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“…For example, permeabilities of compressed foams as high as 8 Â 10 À 6 m 2 and for a 1 mm thick foam layer the equivalent Darcy number is equal to 8 (see Nield et al [36] and references therein). For a high porosity porous medium (e ¼0.972), Givler and Altobelli [37] have determined experimentally thatm f ¼ 7:5 þ 3:4 À2:4 m f , wherem f is the effective viscosity and m f is the fluid viscosity. Accordingly, the flow in the porous medium is described by the Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective or Brinkman viscosity.…”

Section: Introductionmentioning

confidence: 99%

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

Nanjundappa¹,

Shivakumara

Prakash

2012

Journal of Magnetism and Magnetic Materials

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a b s t r a c tA model for penetrative ferroconvection via internal heat generation in a ferrofluid saturated porous layer is explored. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-paramagnetic and insulated to temperature perturbations, while at upper stress-free boundary a general convective-radiative exchange condition on perturbed temperature is imposed. The resulting eigenvalue problem is solved numerically using the Galerkin method. It is found that increasing in the dimensionless heat source strength N s , magnetic number M 1 Darcy number Da and the non-linearity of magnetization parameter M 3 is to hasten, while increase in the ratio of viscosities L, Biot number Bi and magnetic susceptibility w is to delay the onset of ferroconvection.Further, increase in Bi, Da À 1 and N s and decrease in L, M 1 and M 3 is to diminish the dimension of convection cells.

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“…Author details 1 College of Education and Teacher Development, Henan Normal University, Xinxiang, 453007, P.R. China.…”

Section: Competing Interestsmentioning

confidence: 99%

Attractors for the 3D autonomous and nonautonomous Brinkman-Forchheimer equations

Zhang

Wen

2016

Bound Value Probl

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We consider the large-time behavior such as the existence of attractors for the 3D autonomous and nonautonomous Brinkman-Forchheimer equations. By means of the decomposition method we overcome the difficulties for the existence of absorbing sets and asymptotical compactness of the semigroup generated by a global solution to prove the attractors for the autonomous Brinkman-Forchheimer equation. Under suitable assumptions on the external force σ (t, x) and initial data u τ (x), we prove the existence of a uniform attractor for a 3D nonautonomous Brinkman-Forchheimer equation. Moreover, we apply the theory of weak continuity and weak convergence method to establish the asymptotical compactness of the processes.

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A determination of the effective viscosity for the Brinkman–Forchheimer flow model

Cited by 283 publications

References 12 publications

On the effects of exothermicity and endothermicity upon the temperature fields in a partially-filled porous channel

On the effects of exothermicity and endothermicity upon the temperature fields in a partially-filled porous channel

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

Attractors for the 3D autonomous and nonautonomous Brinkman-Forchheimer equations

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