American Journal of Applied Mathematics

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Hydro-Magnetic Mixed Convection Flow in a Lid-Driven Cavity with Wavy Bottom Surface

Received: 11 November 2014    Accepted: 12 November 2014    Published: 29 November 2014
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Abstract

Mixed convection flow in the presence of magnetic field is examined in a lid-driven cavity with wavy bottom surface. The magnetic field is applied in perpendicular direction to the cavity. Moreover, the cavity is heated from top while the bottom surface is taken as a wavy pattern. The vertical walls of the cavity are adiabatic. The governing equations have been solved by using Galerkin weighted residual method of finite element formulation. To uncover the flow patterns and heat transfer mechanisms within the cavity, the results are presented in terms of streamlines and isotherms for different Reynolds number, Grashof number, Hartmann number and number of undulations offered by the wavy bottom surface. Also the effects of these parameters are shown on the Local Nusselt number. It is observed that the wavy lid-driven cavity can be considered as an effective heat transfer mechanism in presence of magnetic field at larger wavy surface amplitudes and low Richardson numbers.

DOI 10.11648/j.ajam.s.2015030101.12
Published in American Journal of Applied Mathematics (Volume 3, Issue 1-1, January 2015)

This article belongs to the Special Issue Fluid Flow and Heat Transfer Inside a Closed Domain

Page(s) 8-19
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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), 2024. Published by Science Publishing Group

Keywords

Mixed Convection, Lid-Driven Cavity, Magneto-Hydrodynamics, Wavy Surface, Heat Transfer

References
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[2] C. K. Cha, Y. Jaluria, Recirculating mixed convection flow for energy extraction, Int. J. Heat Mass Transfer, Vol. 27, pp. 1801–1810 (1984).
[3] F. J. K. Ideriah, Prediction of turbulent cavity flow driven by buoyancy and shear, J. Mech. Eng. Sci., Vol. 22, pp. 287–295 (1980).
[4] J. Imberger, P.F. Hamblin, Dynamics of lakes, reservoirs, and cooling ponds, Adv. Rev. Fluid Mech., Vol. 14, pp. 153–187 (1982).
[5] K. Khanafer, B. Al-Azmi, A. Marafie, I. Pop, Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure, Int. J. Heat Mass Transfer, Vol. 52, pp. 1887–1896 (2009).
[6] A. Al-Amiri, K. Khanafer, Fluid–structure interaction analysis of mixed convection heat transfer in a lid-driven cavity with a flexible bottom wall, Int. J. Heat and Mass Transfer, Vol. 54, pp. 3826–3836 (2011).
[7] S. S. Mendu, P. K. Das, Fluid flow in a cavity driven by an oscillating lid—A simulation by lattice Boltzmann method, Eur. J. Mech. B Fluids, Vol. 39, 59–70 (2013).
[8] H. F. Oztop, I. Dagtekin, Mixed convection in two-sided lid-driven differentially heated square cavity, Int. J. Heat Mass Transfer, Vol. 49, pp. 1761–1769 (2004).
[9] L. K. Saha, M. C. Somadder, K. M. S. Uddin, Mixed convection heat transfer in a lid driven cavity with wavy bottom surface, Amer. J. Appl. Math., Vol. 1(5), 92–101 (2013).
[10] A. J. Chamkha, Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation or absorption, Num. Heat Transfer, Part A, Vol. 41, pp. 529–546 (2002).
[11] M. M. Rahman, M. A. Alim, M. M. A. Sarker, Numerical study on the conjugate effect of joule heating and magnato-hydrodynamics mixed convection in an obstructed lid-driven square cavity, Int. Comm. Heat Mass Transfer, Vol. 37 (5), pp. 524–534 (2010).
[12] N. Rudraiah, M. Venkatachalappa, C. K. Subbaraya, Combined surface tension and buoyancy-driven convection in a rectangular open cavity in the presence of magnetic field, Int. J. Non-Linear Mech., Vol. 30 (5), pp. 759–770 (1995).
[13] S. Sivasankaran, A. Malleswaran, J. Lee, P. Sundar, Hydro-magnetic combined convection in a lid-driven cavity with sinusoidal boundary conditions on both sidewalls, Int. J. Heat Mass Transfer, Vol. 54, 512–525 (2011).
[14] A. Al-Amiri, K. Khanafer, I. Pop, Numerical simulation of unsteady mixed convection in a driven cavity using an externally excited sliding lid, Int. J. Heat Mass Transfer, Vol. 50, pp. 1771–1780 (2007).
Author Information
  • Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh

  • Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

  • Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

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  • APA Style

    Litan Kumar Saha, Monotos Chandra Somadder, Nepal Chandra Roy. (2014). Hydro-Magnetic Mixed Convection Flow in a Lid-Driven Cavity with Wavy Bottom Surface. American Journal of Applied Mathematics, 3(1-1), 8-19. https://doi.org/10.11648/j.ajam.s.2015030101.12

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    ACS Style

    Litan Kumar Saha; Monotos Chandra Somadder; Nepal Chandra Roy. Hydro-Magnetic Mixed Convection Flow in a Lid-Driven Cavity with Wavy Bottom Surface. Am. J. Appl. Math. 2014, 3(1-1), 8-19. doi: 10.11648/j.ajam.s.2015030101.12

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    AMA Style

    Litan Kumar Saha, Monotos Chandra Somadder, Nepal Chandra Roy. Hydro-Magnetic Mixed Convection Flow in a Lid-Driven Cavity with Wavy Bottom Surface. Am J Appl Math. 2014;3(1-1):8-19. doi: 10.11648/j.ajam.s.2015030101.12

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  • @article{10.11648/j.ajam.s.2015030101.12,
      author = {Litan Kumar Saha and Monotos Chandra Somadder and Nepal Chandra Roy},
      title = {Hydro-Magnetic Mixed Convection Flow in a Lid-Driven Cavity with Wavy Bottom Surface},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {1-1},
      pages = {8-19},
      doi = {10.11648/j.ajam.s.2015030101.12},
      url = {https://doi.org/10.11648/j.ajam.s.2015030101.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.s.2015030101.12},
      abstract = {Mixed convection flow in the presence of magnetic field is examined in a lid-driven cavity with wavy bottom surface. The magnetic field is applied in perpendicular direction to the cavity. Moreover, the cavity is heated from top while the bottom surface is taken as a wavy pattern. The vertical walls of the cavity are adiabatic. The governing equations have been solved by using Galerkin weighted residual method of finite element formulation. To uncover the flow patterns and heat transfer mechanisms within the cavity, the results are presented in terms of streamlines and isotherms for different Reynolds number, Grashof number, Hartmann number and number of undulations offered by the wavy bottom surface. Also the effects of these parameters are shown on the Local Nusselt number. It is observed that the wavy lid-driven cavity can be considered as an effective heat transfer mechanism in presence of magnetic field at larger wavy surface amplitudes and low Richardson numbers.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - Hydro-Magnetic Mixed Convection Flow in a Lid-Driven Cavity with Wavy Bottom Surface
    AU  - Litan Kumar Saha
    AU  - Monotos Chandra Somadder
    AU  - Nepal Chandra Roy
    Y1  - 2014/11/29
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    N1  - https://doi.org/10.11648/j.ajam.s.2015030101.12
    DO  - 10.11648/j.ajam.s.2015030101.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 8
    EP  - 19
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.s.2015030101.12
    AB  - Mixed convection flow in the presence of magnetic field is examined in a lid-driven cavity with wavy bottom surface. The magnetic field is applied in perpendicular direction to the cavity. Moreover, the cavity is heated from top while the bottom surface is taken as a wavy pattern. The vertical walls of the cavity are adiabatic. The governing equations have been solved by using Galerkin weighted residual method of finite element formulation. To uncover the flow patterns and heat transfer mechanisms within the cavity, the results are presented in terms of streamlines and isotherms for different Reynolds number, Grashof number, Hartmann number and number of undulations offered by the wavy bottom surface. Also the effects of these parameters are shown on the Local Nusselt number. It is observed that the wavy lid-driven cavity can be considered as an effective heat transfer mechanism in presence of magnetic field at larger wavy surface amplitudes and low Richardson numbers.
    VL  - 3
    IS  - 1-1
    ER  - 

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