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Simulating Mixed Convection in a Lid-Driven Wavy Enclosure with Block in Different Locations

Received: 17 November 2023    Accepted: 4 December 2023    Published: 11 December 2023
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Abstract

Mixed convection in a wavy enclosure driven by a lid and including rectangular shaped blocks at various positions is the focus of this paper's simulation investigation. In this investigation, we also looked at how the heat transfer enhancement changed depending on the orientation of the heated block in relation to the stream. The control equations for mass, thermal energy, and Navier-Stokes are solved numerically using the Galerkin weighted residual finite element method. The enclosure contains two rectangular shaped heated blocks strategically positioned at varying heights - one set closer to the lower section of the enclosure, another situated at the mid-section of the enclosure and final set closer to upper wavy surface. The thermal insulation property of the wavy top wall, coupled with active heating of the bottom wall and blocks, creates a dynamic convective environment. Also, the lid-generated flow is driven by the left wall moving upwards and the right wall moving downwards. Richardson number impacts on streamlines, isotherms, dimensionless temperature, velocity profiles, average Nusselt numbers, and other characteristics are investigated in this study. Visualizations of these impacts are made possible using graphics. Inside the container, two eddies spun counterclockwise in every instance. Regardless of other factors, a higher rotating speed yields better performance. Enhanced heat transport would also be the outcome of a well-balanced set of regulating factors.

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 9, Issue 2)
DOI 10.11648/j.ijfmts.20230902.11
Page(s) 20-28
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), 2024. Published by Science Publishing Group

Keywords

Mixed Convection, Lid-Driven, Wavy Top, FEM and Heated Blocks

References
[1] F. M. Azizul, A. I. Alsabry, I. Hashim, and A. J. Chamkha, "Heatline Visualization of Mixed Convection inside Double Lid-Driven Cavity having Heated Wavy Wall," Journal of Thermal Analysis and Calorimetry, vol. 145, pp. 3159-3176, 2020.
[2] S. Jani, M. Mahmoodi, and M. Amini, "Magnetohydrodynamic Free Convection in a Square Cavity Heated from Below and Cooled from Other Walls," International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, vol. 7, pp. 750-755, 2013.
[3] Y. C. Ching, H. F. Öztop, M. M. Rahman, M. R. Islam, and A. Ahsan, "Finite Element Simulation of Mixed Convection Heat and Mass Transfer in a Right Triangular Enclosure," Int. J Heat Mass Transf., vol. 39, no. 5, pp. 689-696, May 2012.
[4] S. A. Hossain, M. A. Alim, and S. K. Saha, "A Finite Element Analysis on MHD Free Convection Flow in Open Square Cavity Containing Heated Circular Cylinder," American Journal of Computational Mathematics, vol. 5, pp. 41-54, 2015.
[5] D. S. Kumar, A. K. Dass, and A. Dewan, "Analysis of Non-Darcy Models for Mixed Convection in a Porous Cavity using a Multigrid Approach," Numer. Heat Transfer, vol. 56, no. 8, pp. 685-708, 2009.
[6] D. Senthil Kumar, K. Murugesan, and H. R. Thomas, "Numerical Simulation of Double Diffusive Mixed Convection in a Lid-Driven Square Cavity using Velocity-Vorticity Formulation," Numer. Heat Transfer A, vol. 54, no. 9, pp. 837-865, 2008.
[7] M. M. Rahman, M. Elias, and M. A. Alim, "Mixed Convection Flow in a Rectangular Ventilated Cavity with a Heat-Conducting Square Cylinder at the Center," Journal of Engineering and Applied Sciences, vol. 4, no. 5, pp. 20-29, 2009.
[8] S. Mahjabin and M. A. Alim, "Effect of Hartmann Number on Free Convective Flow of MHD Fluid in a Square Cavity with a Heated Cone of Different Orientation," American Journal of Computational Mathematics, vol. 8, pp. 314-325, 2018.
[9] A. J. Chamkha, "Hydromagnetic Combined Convection Flow in a Vertical Lid-Driven Cavity with Internal Heat Generation or Absorption," Numerical Heat Transfer, Part A, vol. 41, pp. 529-546, 2002.
[10] A. K. Prasad and J. R. Koseff, "Combined Forced and Natural Convection Heat Transfer in a Deep Lid-Driven Cavity Flow," International Journal of Heat and Fluid Flow, vol. 17, pp. 460-467, 1996.
[11] M. J. H. Munshi, M. A. Alim, A. H. Bhuiyan and K. F. U. Ahmed,“Numerical simulation of mixed convection heat transfers of nanofluid in a lid-driven porous medium square enclosure”, American Institute of Physics (AIP), Vol. 2121, pp. 030005- (1-9), 2019.
[12] M. J. H. Munshi, M. A. Alim, A. H. Bhuiyan and M. Ali, “Hydrodynamic mixed convection in a lid-drivensquare cavity including elliptic shape heated block with corner heater”, American Institute of Physics (AIP), Vol. 194, pp. 442- 449, 2017.
[13] M. J. H. Munshi, M. A. Alim, A. H. Bhuiyan, M. Ali,“Optimization of Mixed convection in a lid-driven porous square cavity with internal elliptic shape adiabatic block and linearly heated side walls”, American Institute of Physics (AIP), 1851, 020049; doi: 10.1063/1.4984678, 2017.
[14] M. M. Islam, M. A. Alim, M. M. Alam, M. J. H. Munshi, “Simulation of Natural Convection flow with Magneto-Hytrodynamics in a wavy top enclosure with a semi-Circular heater”, Open Journal of Applied Sciences, Scientific Research Publicising, Vol. 13, pp. 591-603, 2023.
[15] M. J. H. Munshi, G. Mostafa, A, B. S, M. Munshi., M. Waliullah, “ Hydrodynamic Mixed Convection in a Lid-driven hexagonal cavity with corner heater”, American Journal of Computational Mathematics, Scientific Research Publicising, Vol. 8, No. 245- 258, 2018.
[16] J. N. Reddy, "An Introduction to Finite Element Method," McGraw-Hill, New York, 1993.
[17] O. C. Zienkiewicz and R. L. Taylor, "The finite element method," Fourth Ed., McGraw-Hill, 1991.
Cite This Article
  • APA Style

    Pradip Kumer Sarker, S., Mahmud Alam, M., Jahirul Haque Munshi, M. (2023). Simulating Mixed Convection in a Lid-Driven Wavy Enclosure with Block in Different Locations. International Journal of Fluid Mechanics & Thermal Sciences, 9(2), 20-28. https://doi.org/10.11648/j.ijfmts.20230902.11

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    ACS Style

    Pradip Kumer Sarker, S.; Mahmud Alam, M.; Jahirul Haque Munshi, M. Simulating Mixed Convection in a Lid-Driven Wavy Enclosure with Block in Different Locations. Int. J. Fluid Mech. Therm. Sci. 2023, 9(2), 20-28. doi: 10.11648/j.ijfmts.20230902.11

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    AMA Style

    Pradip Kumer Sarker S, Mahmud Alam M, Jahirul Haque Munshi M. Simulating Mixed Convection in a Lid-Driven Wavy Enclosure with Block in Different Locations. Int J Fluid Mech Therm Sci. 2023;9(2):20-28. doi: 10.11648/j.ijfmts.20230902.11

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  • @article{10.11648/j.ijfmts.20230902.11,
      author = {Sree Pradip Kumer Sarker and Mohammad Mahmud Alam and Mohammod Jahirul Haque Munshi},
      title = {Simulating Mixed Convection in a Lid-Driven Wavy Enclosure with Block in Different Locations},
      journal = {International Journal of Fluid Mechanics & Thermal Sciences},
      volume = {9},
      number = {2},
      pages = {20-28},
      doi = {10.11648/j.ijfmts.20230902.11},
      url = {https://doi.org/10.11648/j.ijfmts.20230902.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20230902.11},
      abstract = {Mixed convection in a wavy enclosure driven by a lid and including rectangular shaped blocks at various positions is the focus of this paper's simulation investigation. In this investigation, we also looked at how the heat transfer enhancement changed depending on the orientation of the heated block in relation to the stream. The control equations for mass, thermal energy, and Navier-Stokes are solved numerically using the Galerkin weighted residual finite element method. The enclosure contains two rectangular shaped heated blocks strategically positioned at varying heights - one set closer to the lower section of the enclosure, another situated at the mid-section of the enclosure and final set closer to upper wavy surface. The thermal insulation property of the wavy top wall, coupled with active heating of the bottom wall and blocks, creates a dynamic convective environment. Also, the lid-generated flow is driven by the left wall moving upwards and the right wall moving downwards. Richardson number impacts on streamlines, isotherms, dimensionless temperature, velocity profiles, average Nusselt numbers, and other characteristics are investigated in this study. Visualizations of these impacts are made possible using graphics. Inside the container, two eddies spun counterclockwise in every instance. Regardless of other factors, a higher rotating speed yields better performance. Enhanced heat transport would also be the outcome of a well-balanced set of regulating factors.
    },
     year = {2023}
    }
    

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  • TY  - JOUR
    T1  - Simulating Mixed Convection in a Lid-Driven Wavy Enclosure with Block in Different Locations
    AU  - Sree Pradip Kumer Sarker
    AU  - Mohammad Mahmud Alam
    AU  - Mohammod Jahirul Haque Munshi
    Y1  - 2023/12/11
    PY  - 2023
    N1  - https://doi.org/10.11648/j.ijfmts.20230902.11
    DO  - 10.11648/j.ijfmts.20230902.11
    T2  - International Journal of Fluid Mechanics & Thermal Sciences
    JF  - International Journal of Fluid Mechanics & Thermal Sciences
    JO  - International Journal of Fluid Mechanics & Thermal Sciences
    SP  - 20
    EP  - 28
    PB  - Science Publishing Group
    SN  - 2469-8113
    UR  - https://doi.org/10.11648/j.ijfmts.20230902.11
    AB  - Mixed convection in a wavy enclosure driven by a lid and including rectangular shaped blocks at various positions is the focus of this paper's simulation investigation. In this investigation, we also looked at how the heat transfer enhancement changed depending on the orientation of the heated block in relation to the stream. The control equations for mass, thermal energy, and Navier-Stokes are solved numerically using the Galerkin weighted residual finite element method. The enclosure contains two rectangular shaped heated blocks strategically positioned at varying heights - one set closer to the lower section of the enclosure, another situated at the mid-section of the enclosure and final set closer to upper wavy surface. The thermal insulation property of the wavy top wall, coupled with active heating of the bottom wall and blocks, creates a dynamic convective environment. Also, the lid-generated flow is driven by the left wall moving upwards and the right wall moving downwards. Richardson number impacts on streamlines, isotherms, dimensionless temperature, velocity profiles, average Nusselt numbers, and other characteristics are investigated in this study. Visualizations of these impacts are made possible using graphics. Inside the container, two eddies spun counterclockwise in every instance. Regardless of other factors, a higher rotating speed yields better performance. Enhanced heat transport would also be the outcome of a well-balanced set of regulating factors.
    
    VL  - 9
    IS  - 2
    ER  - 

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Author Information
  • Department of Mathematics, Dhaka University of Engineering and Technology (DUET), Gazipur, Bangladesh

  • Department of Mathematics, Dhaka University of Engineering and Technology (DUET), Gazipur, Bangladesh

  • Department of Mathematics, Hamdard University Bangladesh, Munshigonj, Bangladesh

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