Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces

A. J. Keikha

doi:doi:10.11648/j.cbe.20170203.13

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Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces

A. J. Keikha

Published in Chemical and Biomolecular Engineering (Volume 2, Issue 3)

Received: 16 January 2017 Accepted: 13 March 2017 Published: 24 April 2017

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Abstract

The present study deals with the effect of electromagnetic forces on the problem of natural convection in a cavity of small aspect ratio with differentially heated end walls. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A→ 0, are derived.

Published in	Chemical and Biomolecular Engineering (Volume 2, Issue 3)
DOI	10.11648/j.cbe.20170203.13
Page(s)	142-151
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Magnetohydrodynamics, Analytical Solution, Natural Convection, Laminar Flow, Boundary Layer

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APA Style

A. J. Keikha. (2017). Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces. Chemical and Biomolecular Engineering, 2(3), 142-151. https://doi.org/10.11648/j.cbe.20170203.13

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ACS Style

A. J. Keikha. Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces. Chem. Biomol. Eng. 2017, 2(3), 142-151. doi: 10.11648/j.cbe.20170203.13

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AMA Style

A. J. Keikha. Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces. Chem Biomol Eng. 2017;2(3):142-151. doi: 10.11648/j.cbe.20170203.13

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@article{10.11648/j.cbe.20170203.13,
  author = {A. J. Keikha},
  title = {Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces},
  journal = {Chemical and Biomolecular Engineering},
  volume = {2},
  number = {3},
  pages = {142-151},
  doi = {10.11648/j.cbe.20170203.13},
  url = {https://doi.org/10.11648/j.cbe.20170203.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbe.20170203.13},
  abstract = {The present study deals with the effect of electromagnetic forces on the problem of natural convection in a cavity of small aspect ratio with differentially heated end walls. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A→ 0, are derived.},
 year = {2017}
}

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TY  - JOUR
T1  - Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces
AU  - A. J. Keikha
Y1  - 2017/04/24
PY  - 2017
N1  - https://doi.org/10.11648/j.cbe.20170203.13
DO  - 10.11648/j.cbe.20170203.13
T2  - Chemical and Biomolecular Engineering
JF  - Chemical and Biomolecular Engineering
JO  - Chemical and Biomolecular Engineering
SP  - 142
EP  - 151
PB  - Science Publishing Group
SN  - 2578-8884
UR  - https://doi.org/10.11648/j.cbe.20170203.13
AB  - The present study deals with the effect of electromagnetic forces on the problem of natural convection in a cavity of small aspect ratio with differentially heated end walls. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A→ 0, are derived.
VL  - 2
IS  - 3
ER  -

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Author Information

A. J. Keikha

Faculty of Marine Engineering, Chabahar Maritime University, Chabahar, Iran

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APA Style

A. J. Keikha. (2017). Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces. Chemical and Biomolecular Engineering, 2(3), 142-151. https://doi.org/10.11648/j.cbe.20170203.13

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ACS Style

A. J. Keikha. Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces. Chem. Biomol. Eng. 2017, 2(3), 142-151. doi: 10.11648/j.cbe.20170203.13

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AMA Style

A. J. Keikha. Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces. Chem Biomol Eng. 2017;2(3):142-151. doi: 10.11648/j.cbe.20170203.13

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@article{10.11648/j.cbe.20170203.13,
  author = {A. J. Keikha},
  title = {Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces},
  journal = {Chemical and Biomolecular Engineering},
  volume = {2},
  number = {3},
  pages = {142-151},
  doi = {10.11648/j.cbe.20170203.13},
  url = {https://doi.org/10.11648/j.cbe.20170203.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbe.20170203.13},
  abstract = {The present study deals with the effect of electromagnetic forces on the problem of natural convection in a cavity of small aspect ratio with differentially heated end walls. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A→ 0, are derived.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated end Walls in Presence of Electromagnetic Forces
AU  - A. J. Keikha
Y1  - 2017/04/24
PY  - 2017
N1  - https://doi.org/10.11648/j.cbe.20170203.13
DO  - 10.11648/j.cbe.20170203.13
T2  - Chemical and Biomolecular Engineering
JF  - Chemical and Biomolecular Engineering
JO  - Chemical and Biomolecular Engineering
SP  - 142
EP  - 151
PB  - Science Publishing Group
SN  - 2578-8884
UR  - https://doi.org/10.11648/j.cbe.20170203.13
AB  - The present study deals with the effect of electromagnetic forces on the problem of natural convection in a cavity of small aspect ratio with differentially heated end walls. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A→ 0, are derived.
VL  - 2
IS  - 3
ER  -

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