Heat or mass transfer from a sphere in Stokes flow at low Péclet number

Christopher G. Bell; Helen M. Byrne; Jonathan P. Whiteley; Sarah L. Waters

doi:10.1016/j.aml.2012.10.010

Heat or mass transfer from a sphere in Stokes flow at low Péclet number

Christopher G. Bell, Helen M. Byrne, Jonathan P. Whiteley, Sarah L. Waters

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We consider the low Péclet number, Pe≪1, asymptotic solution for steady-state heat or mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of Van Dyke's rule up to terms of O(Pe3) shows that the O(Pe3logPe) terms in the expression for the average Nusselt/Sherwood number are twice those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase the range of validity of the expansion. © 2012 Elsevier Ltd. All rights reserved.

Original language	English (US)
Pages (from-to)	392-396
Number of pages	5
Journal	Applied Mathematics Letters
Volume	26
Issue number	4
DOIs	https://doi.org/10.1016/j.aml.2012.10.010
State	Published - Apr 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). SLW is grateful for funding from the EPSRC in the form of an Advanced Research Fellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.aml.2012.10.010

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title = "Heat or mass transfer from a sphere in Stokes flow at low P{\'e}clet number",

abstract = "We consider the low P{\'e}clet number, Pe≪1, asymptotic solution for steady-state heat or mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of Van Dyke's rule up to terms of O(Pe3) shows that the O(Pe3logPe) terms in the expression for the average Nusselt/Sherwood number are twice those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase the range of validity of the expansion. {\textcopyright} 2012 Elsevier Ltd. All rights reserved.",

author = "Bell, {Christopher G.} and Byrne, {Helen M.} and Whiteley, {Jonathan P.} and Waters, {Sarah L.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). SLW is grateful for funding from the EPSRC in the form of an Advanced Research Fellowship. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1016/j.aml.2012.10.010",

language = "English (US)",

volume = "26",

pages = "392--396",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

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T1 - Heat or mass transfer from a sphere in Stokes flow at low Péclet number

AU - Bell, Christopher G.

AU - Byrne, Helen M.

AU - Whiteley, Jonathan P.

AU - Waters, Sarah L.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). SLW is grateful for funding from the EPSRC in the form of an Advanced Research Fellowship. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013/4

Y1 - 2013/4

N2 - We consider the low Péclet number, Pe≪1, asymptotic solution for steady-state heat or mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of Van Dyke's rule up to terms of O(Pe3) shows that the O(Pe3logPe) terms in the expression for the average Nusselt/Sherwood number are twice those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase the range of validity of the expansion. © 2012 Elsevier Ltd. All rights reserved.

AB - We consider the low Péclet number, Pe≪1, asymptotic solution for steady-state heat or mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of Van Dyke's rule up to terms of O(Pe3) shows that the O(Pe3logPe) terms in the expression for the average Nusselt/Sherwood number are twice those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase the range of validity of the expansion. © 2012 Elsevier Ltd. All rights reserved.

UR - http://hdl.handle.net/10754/598449

UR - https://linkinghub.elsevier.com/retrieve/pii/S0893965912004429

UR - http://www.scopus.com/inward/record.url?scp=84872595963&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2012.10.010

DO - 10.1016/j.aml.2012.10.010

M3 - Article

SN - 0893-9659

VL - 26

SP - 392

EP - 396

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 4

ER -

Heat or mass transfer from a sphere in Stokes flow at low Péclet number

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