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Analysis of MHD Mixed Convection Flow Within a Square Enclosure Containing a Triangular Obstacle

Received: 15 October 2015     Accepted: 29 October 2015     Published: 8 December 2015
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Abstract

Finite element method is used to solve two-dimensional governing mass, momentum and energy equations for steady state, mixed convection problem inside a lid driven square enclosure containing a triangular hot obstacle located at the centre of the enclosure. The enclosure top wall is adiabatic while the bottom wall and triangular obstacle are maintained at a uniform temperature higher than the vertical side walls. The left vertical wall is moving with a uniform velocity by unity from bottom to top. All solid boundaries are in no slip condition. The aim of the study is to describe the effect of magnetic field, Prandtl number and the size of triangular obstacle on mixed convection fluid flow, heat transfer and temperature of the fluid. The investigation is conducted for various values of magnetic parameter Ha, obstacle size (area) A, Richardson number Ri, and Prandtl number Pr. Various results such as streamlines, isotherms, heat transfer rates in terms of average Nusselt number Nu, and average temperature θav of the fluid in the enclosure are presented for different parameters. It is observed that the obstacle size and dimensionless parameters Ha and Pr have significant effect on both the flow and thermal fields. The results also indicate that the average Nusselt number at the heated surface is strongly dependent on the configurations of the system studied under different geometrical and physical configurations.

Published in American Journal of Applied Mathematics (Volume 3, Issue 6)
DOI 10.11648/j.ajam.20150306.18
Page(s) 288-296
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), 2015. Published by Science Publishing Group

Keywords

Magnetohydrodynamic, Mixed Convection, Square Enclosure, Triangular Obstacle

References
[1] Alchaar, S., Vasseur, P., Bilgen, E., 1995. Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field,” Journal of Heat Transfer, 117 (3), pp. 668-673.
[2] Akhter, T., Alim, M.A., 2010. Effects of pressure work on natural convection flow around a sphere with radiation heat loss. Nonlinear Analysis: Modeling and Control, vol. 15, No. 3, 287-298.
[3] Mousa, M.M. 2010. Modeling of laminar buoyancy convection in a square cavity containing an obstacle. Mathematics Subject Classification: 65M60, 76D05, 80A20.
[4] Nasrin, R., 2011. Mixed magnetoconvection in a lid driven cavity with a sinusoidal wavy wall and a central heat conducting body. Journal of Naval Architecture and Marine Engineering. DOI: 10.3329/ jname.v8il.6793.
[5] Aydin, O. The effects of moving wall on Aiding and opposing mechanisms of mixed convection in a shear and buoyancy driven cavity. Int. Commun. Heat and Mass Transfer 26 (1999) 1019-1028.
[6] Oztop, H.F., Dagtekin, I, 2004. Mixed convection in two-sided lid-driven differentially heated square cavity. Int. J. Heat Mass Transfer 47, 1761-1769.
[7] Saha, L.K., Somadder, M.C., Salah Uddin, K.M. 2013. Mixed convection heat transfer in a lid driven cavity with wavy bottom surface. American Journal of Applied Mathematics 1(5): 92-101.
[8] Oztop, H.F. Al-Salem, K. Pop, L., 2011. MHD mixed convection in a lid-driven cavity with corner heater. International Journal of Heat and Mass Transfer vol. 54, pp. 3494-3504.
[9] Rahman, M. M., Alim, M. A., 2010. MHD mixed convection flow in a vertical lid-driven square enclosure including a heat conducting horizontal circular cylinder with Joule heating. Nonlinear Analysis: Modeling and Control, Vol. 15, No. 2, 199-211.
[10] Moallemi, M. K., Jang, K. S., 1992. Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity. Int. J. Heat Mass Tran., 35, pp. 1881-1892.
[11] Prasad, A.K., Koseff, J.R., 1996. Combined forced and natural convection heat transfer in a deep lid-driven cavity flow. Int J. Heat and Fluid Flow., vol. 17, pp. 460-467.
[12] Yadollahi Farsani, R., Ghasemi, B., 2011. Magnetohydrodynamic mixed convective flow in a cavity. World Academy of Science, Engineering and Technology. Vol 5, 11-21.
[13] Taylor, C, Hood, P. A. numerical solution of the Navier-Stokes equations using finite element technique, Computers & Fluids 1 (1) (1973) 73-89.
[14] Dechaumphai, P. Finite Element Method in Engineering, 2nd ed. Chulalongkorn University Press, Bangkok, 1999.
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  • APA Style

    Kakali Chowdhury, Md. Abdul Alim. (2015). Analysis of MHD Mixed Convection Flow Within a Square Enclosure Containing a Triangular Obstacle. American Journal of Applied Mathematics, 3(6), 288-296. https://doi.org/10.11648/j.ajam.20150306.18

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    ACS Style

    Kakali Chowdhury; Md. Abdul Alim. Analysis of MHD Mixed Convection Flow Within a Square Enclosure Containing a Triangular Obstacle. Am. J. Appl. Math. 2015, 3(6), 288-296. doi: 10.11648/j.ajam.20150306.18

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    AMA Style

    Kakali Chowdhury, Md. Abdul Alim. Analysis of MHD Mixed Convection Flow Within a Square Enclosure Containing a Triangular Obstacle. Am J Appl Math. 2015;3(6):288-296. doi: 10.11648/j.ajam.20150306.18

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  • @article{10.11648/j.ajam.20150306.18,
      author = {Kakali Chowdhury and Md. Abdul Alim},
      title = {Analysis of MHD Mixed Convection Flow Within a Square Enclosure Containing a Triangular Obstacle},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {6},
      pages = {288-296},
      doi = {10.11648/j.ajam.20150306.18},
      url = {https://doi.org/10.11648/j.ajam.20150306.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.18},
      abstract = {Finite element method is used to solve two-dimensional governing mass, momentum and energy equations for steady state, mixed convection problem inside a lid driven square enclosure containing a triangular hot obstacle located at the centre of the enclosure. The enclosure top wall is adiabatic while the bottom wall and triangular obstacle are maintained at a uniform temperature higher than the vertical side walls. The left vertical wall is moving with a uniform velocity by unity from bottom to top. All solid boundaries are in no slip condition. The aim of the study is to describe the effect of magnetic field, Prandtl number and the size of triangular obstacle on mixed convection fluid flow, heat transfer and temperature of the fluid. The investigation is conducted for various values of magnetic parameter Ha, obstacle size (area) A, Richardson number Ri, and Prandtl number Pr. Various results such as streamlines, isotherms, heat transfer rates in terms of average Nusselt number Nu, and average temperature θav of the fluid in the enclosure are presented for different parameters. It is observed that the obstacle size and dimensionless parameters Ha and Pr have significant effect on both the flow and thermal fields. The results also indicate that the average Nusselt number at the heated surface is strongly dependent on the configurations of the system studied under different geometrical and physical configurations.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Analysis of MHD Mixed Convection Flow Within a Square Enclosure Containing a Triangular Obstacle
    AU  - Kakali Chowdhury
    AU  - Md. Abdul Alim
    Y1  - 2015/12/08
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajam.20150306.18
    DO  - 10.11648/j.ajam.20150306.18
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 288
    EP  - 296
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20150306.18
    AB  - Finite element method is used to solve two-dimensional governing mass, momentum and energy equations for steady state, mixed convection problem inside a lid driven square enclosure containing a triangular hot obstacle located at the centre of the enclosure. The enclosure top wall is adiabatic while the bottom wall and triangular obstacle are maintained at a uniform temperature higher than the vertical side walls. The left vertical wall is moving with a uniform velocity by unity from bottom to top. All solid boundaries are in no slip condition. The aim of the study is to describe the effect of magnetic field, Prandtl number and the size of triangular obstacle on mixed convection fluid flow, heat transfer and temperature of the fluid. The investigation is conducted for various values of magnetic parameter Ha, obstacle size (area) A, Richardson number Ri, and Prandtl number Pr. Various results such as streamlines, isotherms, heat transfer rates in terms of average Nusselt number Nu, and average temperature θav of the fluid in the enclosure are presented for different parameters. It is observed that the obstacle size and dimensionless parameters Ha and Pr have significant effect on both the flow and thermal fields. The results also indicate that the average Nusselt number at the heated surface is strongly dependent on the configurations of the system studied under different geometrical and physical configurations.
    VL  - 3
    IS  - 6
    ER  - 

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Author Information
  • Electrical and Computer Engineering Department, Presidency University, Dhaka, Bangladesh

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

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