Convection in Porous Media

Nield, D. A.; Bejan, Adrian

doi:10.1007/978-1-4757-3033-3

Cited by 2,321 publications

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“…These and many other examples are described in Nield & Bejan [77], and specific references may be found on pages 238, 239 of Straughan [90].…”

Section: Introductionmentioning

confidence: 93%

“…Let us consider a fluid saturated porous layer occupying the three dimensional layer Darcy's law for convection in a porous medium (see Nield and Bejan (77]) is taken to govern the flow. Defining vi to be the pore averaged velocity in the direction i,…”

Section: Governing Equationsmentioning

confidence: 99%

“…The second is that of Forchheimer (see Nield & Bejan [77]) with non-linear drag terms lvlvi and lvl 2 vi such that 6) where {3 1 and {3 2 are some constants of proportionality.…”

Section: Governing Equationsmentioning

confidence: 99%

“…The study of the stability of such systems of partial differential equations is a key aspect in their physical interpretation (see e.g. Nield & Bejan [77]; Straughan [90]), and continues to be one of the most pursued topics in fluid mechanics.…”

Section: Introductionmentioning

confidence: 99%

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Convection in Porous Media

2013

Convection Heat Transfer

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source• a link is made to the metadata record in Durham E-Theses• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. AbstractThe subject of thermal convection in fluid and porous media is investigated, coupled with the development of efficient spectral finite element methods to improve on the more commonly used techniques for these types of problems.Convection induced by the selective absorption of radiation in a porous medium is DeclarationThe work in this thesis is based on research carried out at the Numerical Analysis

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“…These and many other examples are described in Nield & Bejan [77], and specific references may be found on pages 238, 239 of Straughan [90].…”

Section: Introductionmentioning

confidence: 93%

Section: Governing Equationsmentioning

confidence: 99%

“…The second is that of Forchheimer (see Nield & Bejan [77]) with non-linear drag terms lvlvi and lvl 2 vi such that 6) where {3 1 and {3 2 are some constants of proportionality.…”

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Convection in Porous Media

2013

Convection Heat Transfer

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“…The model (1)-(2) with the pressure term of the form ∇( ) has been proposed in [3,Section 2.2]. For the derivation of the equations, their limitations, modelling, and homogenization questions in porous media we refer to [4][5][6][7][8][9] and [10,Chapter 1].…”

Section: Introductionmentioning

confidence: 99%

Solvability of the Brinkman-Forchheimer-Darcy Equation

Skrzypacz

Wei

2017

Journal of Applied Mathematics

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The nonlinear Brinkman-Forchheimer-Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with variable porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy's range.

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Characterization of fluid-flow resistance in root cultures with a convective flow tubular bioreactor

Carvalho

Curtis

1998

Biotechnol. Bioeng.

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Agrobacterium transformed root cultures of Hyoscyamus muticus were grown in a recirculating 2 L tubular bioreactor system. Performance of this convective flow reactor (CFR) was compared to a bubble column (BC) reactor of the same geometry: replicated CFR experiments produced an average tissue concentration of 556 ± 4 grams fresh weight per liter in 30 d whereas the bubble column produced only 328 ± 5 grams per liter corresponding to 25.3 ± 0.0 and 14.3 ± 0.5 grams dry weight per liter, respectively. Because media nutrient levels were maintained sufficiently high to saturate growth rate, the improved performance of the CFR is attributed to enhanced convective mass transfer. The pressure drops observed for flow through roots grown within the reactors were more than an order of magnitude higher than previously obtained by placing roots grown in shake culture into defined geometries. The experimentally observed flow resistance was much higher than would be predicted from correlations using the root diameter as the characteristic diameter for flow resistance. Several lines of evidence suggest that root hairs are a substantial contributor to the observed high flow resistance in these transformed root cultures. Pressure drop increased nonlinearly with velocity which could not be adequately described by a modified form of the Ergun equation. Kyan et al's (1970) equation, although predicting such curvature, relies almost exclusively on an empirical packing deflection term to describe the hydrodynamic behavior. Implications of these results to the design of submerged reactor systems for root culture are discussed. © 1998 John Wiley & Sons, Inc. Biotechnol Bioeng 60: 375–384, 1998.

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Convection in Porous Media

Cited by 2,321 publications

References 0 publications

Convection in Porous Media

Convection in Porous Media

Solvability of the Brinkman-Forchheimer-Darcy Equation

Characterization of fluid-flow resistance in root cultures with a convective flow tubular bioreactor

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