Heat or mass transfer at low Péclet number for Brinkman and Darcy flow round a sphere

Handle URI:
http://hdl.handle.net/10754/598448
Title:
Heat or mass transfer at low Péclet number for Brinkman and Darcy flow round a sphere
Authors:
Bell, Christopher G.; Byrne, H.M.; Whiteley, J.P.; Waters, S.L.
Abstract:
Prior research into the effect of convection on steady-state mass transfer from a spherical particle embedded in a porous medium has used the Darcy model to describe the flow. However, a limitation of the Darcy model is that it does not account for viscous effects near boundaries. Brinkman modified the Darcy model to include these effects by introducing an extra viscous term. Here we investigate the impact of this extra viscous term on the steady-state mass transfer from a sphere at low Péclet number, Pe 1. We use singular perturbation techniques to find the approximate asymptotic solution for the concentration profile. Mass-release from the surface of the sphere is described by a Robin boundary condition, which represents a first-order chemical reaction. We find that a larger Brinkman viscous boundary layer renders mass transport by convection less effective, and reduces the asymmetry in the peri-sphere concentration profiles. We provide simple analytical expressions that can be used to calculate the concentration profiles, as well as the local and average Sherwood numbers; and comparison to numerical simulations verifies the order of magnitude of the error in the asymptotic expansions. In the appropriate limits, the asymptotic results agree with solutions previously obtained for Stokes and Darcy flow. The solution for Darcy flow with a Robin boundary condition has not been considered previously in the literature and is a new result. Whilst the article has been formulated in terms of mass transfer, the analysis is also applicable to heat transfer, with concentration replaced by temperature and the Sherwood number by the Nusselt number. © 2013 Elsevier Ltd. All rights reserved.
Citation:
Bell CG, Byrne HM, Whiteley JP, Waters SL (2014) Heat or mass transfer at low Péclet number for Brinkman and Darcy flow round a sphere. International Journal of Heat and Mass Transfer 68: 247–258. Available: http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.09.017.
Publisher:
Elsevier BV
Journal:
International Journal of Heat and Mass Transfer
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2014
DOI:
10.1016/j.ijheatmasstransfer.2013.09.017
Type:
Article
ISSN:
0017-9310
Sponsors:
This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBell, Christopher G.en
dc.contributor.authorByrne, H.M.en
dc.contributor.authorWhiteley, J.P.en
dc.contributor.authorWaters, S.L.en
dc.date.accessioned2016-02-25T13:20:53Zen
dc.date.available2016-02-25T13:20:53Zen
dc.date.issued2014-01en
dc.identifier.citationBell CG, Byrne HM, Whiteley JP, Waters SL (2014) Heat or mass transfer at low Péclet number for Brinkman and Darcy flow round a sphere. International Journal of Heat and Mass Transfer 68: 247–258. Available: http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.09.017.en
dc.identifier.issn0017-9310en
dc.identifier.doi10.1016/j.ijheatmasstransfer.2013.09.017en
dc.identifier.urihttp://hdl.handle.net/10754/598448en
dc.description.abstractPrior research into the effect of convection on steady-state mass transfer from a spherical particle embedded in a porous medium has used the Darcy model to describe the flow. However, a limitation of the Darcy model is that it does not account for viscous effects near boundaries. Brinkman modified the Darcy model to include these effects by introducing an extra viscous term. Here we investigate the impact of this extra viscous term on the steady-state mass transfer from a sphere at low Péclet number, Pe 1. We use singular perturbation techniques to find the approximate asymptotic solution for the concentration profile. Mass-release from the surface of the sphere is described by a Robin boundary condition, which represents a first-order chemical reaction. We find that a larger Brinkman viscous boundary layer renders mass transport by convection less effective, and reduces the asymmetry in the peri-sphere concentration profiles. We provide simple analytical expressions that can be used to calculate the concentration profiles, as well as the local and average Sherwood numbers; and comparison to numerical simulations verifies the order of magnitude of the error in the asymptotic expansions. In the appropriate limits, the asymptotic results agree with solutions previously obtained for Stokes and Darcy flow. The solution for Darcy flow with a Robin boundary condition has not been considered previously in the literature and is a new result. Whilst the article has been formulated in terms of mass transfer, the analysis is also applicable to heat transfer, with concentration replaced by temperature and the Sherwood number by the Nusselt number. © 2013 Elsevier Ltd. All rights reserved.en
dc.description.sponsorshipThis publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectBrinkmanen
dc.subjectDarcyen
dc.subjectNusselten
dc.subjectPécleten
dc.subjectSherwooden
dc.subjectSphereen
dc.titleHeat or mass transfer at low Péclet number for Brinkman and Darcy flow round a sphereen
dc.typeArticleen
dc.identifier.journalInternational Journal of Heat and Mass Transferen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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