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

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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Cite This Article
  • 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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    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
  • Faculty of Marine Engineering, Chabahar Maritime University, Chabahar, Iran

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