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Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block

Received: 14 October 2019     Accepted: 9 November 2019     Published: 21 November 2019
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Abstract

In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity.

Published in International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 6)
DOI 10.11648/j.ijtam.20190506.11
Page(s) 74-82
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), 2019. Published by Science Publishing Group

Keywords

Finite Element Method, Numerical Simulation, Natural Convection and Square Block, Rectangular Cavity

References
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[5] M. M. Rahman, M. A. Alim and M. M. A. Sarker“Numerical study on the conjugate effect of Joule heating and magneto hydrodynamics mixed convection in an obstructed lid driven square cavity In heat and mass transfer, 37 (2010), 524-534.
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[13] M. S. Alam, M. S. H. Mollah, A. H. Bhuiyan and M. A. Alim, "Numerical Simulation of Natural Convection in a Rectangular Cavity with Corner Heater in Presence of Magnetic Field", Journal of Computer and Mathematical Sciences, Vol. 8, No. 6, pp 215-225, June 2017.
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Cite This Article
  • APA Style

    Md. Raihanul Haque, Md. Abdul Alim, Md. Mahmud Alam, Md. Shahidul Alam. (2019). Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block. International Journal of Theoretical and Applied Mathematics, 5(6), 74-82. https://doi.org/10.11648/j.ijtam.20190506.11

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    ACS Style

    Md. Raihanul Haque; Md. Abdul Alim; Md. Mahmud Alam; Md. Shahidul Alam. Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block. Int. J. Theor. Appl. Math. 2019, 5(6), 74-82. doi: 10.11648/j.ijtam.20190506.11

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    AMA Style

    Md. Raihanul Haque, Md. Abdul Alim, Md. Mahmud Alam, Md. Shahidul Alam. Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block. Int J Theor Appl Math. 2019;5(6):74-82. doi: 10.11648/j.ijtam.20190506.11

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  • @article{10.11648/j.ijtam.20190506.11,
      author = {Md. Raihanul Haque and Md. Abdul Alim and Md. Mahmud Alam and Md. Shahidul Alam},
      title = {Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {5},
      number = {6},
      pages = {74-82},
      doi = {10.11648/j.ijtam.20190506.11},
      url = {https://doi.org/10.11648/j.ijtam.20190506.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190506.11},
      abstract = {In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block
    AU  - Md. Raihanul Haque
    AU  - Md. Abdul Alim
    AU  - Md. Mahmud Alam
    AU  - Md. Shahidul Alam
    Y1  - 2019/11/21
    PY  - 2019
    N1  - https://doi.org/10.11648/j.ijtam.20190506.11
    DO  - 10.11648/j.ijtam.20190506.11
    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
    SP  - 74
    EP  - 82
    PB  - Science Publishing Group
    SN  - 2575-5080
    UR  - https://doi.org/10.11648/j.ijtam.20190506.11
    AB  - In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity.
    VL  - 5
    IS  - 6
    ER  - 

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Author Information
  • Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh

  • Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

  • Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh

  • Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh

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