International Journal of Applied Mathematics and Theoretical Physics

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Double Lid Driven Cavity with Different Moving Wall Directions for Low Reynolds Number Flow

Received: 14 August 2018    Accepted: 30 August 2018    Published: 15 October 2018
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Abstract

In this paper, a numerical examination used to analyze the flow and heat transfer characteristics inside a double lid-driven cavity underneath buoyancy consequences of thermal diffusion. The lid is due to the movement of the isothermal vertical sidewalls of different constant temperatures, while other walls are kept adiabatic. Also, the upright walls are moving at a constant rate and four different moving wall directions are considered along these walls. Further, the governing equations of the flow and thermal fields are transformed into dimensionless equations and then solved numerically using finite difference method. A contrast of the current learn is additionally carried out with the formerly published works and observed excellent agreement. Moreover, the results from numerical simulations have been presented in the form of velocities and isothermal profiles, shown graphically and discussed for different Reynolds number. Result unveils that, the influence of the development of the velocity profiles in the chamber decreases with the augmentation of Re. Besides, the intensification of Reynolds number ends in forming diminution of thermal boundary layers near the heated wall. In addition, the maximum Average Nusselt number can be obtained when the left lid poignant towards positive direction and the right lid poignant to the same direction.

DOI 10.11648/j.ijamtp.20180403.11
Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 3, September 2018)
Page(s) 67-72
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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

Heat Transfer, Reynolds Number, Nusselt Number, Richardson Number, Prandtl Number

References
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[2] Ghia, U., Ghia, K. N., & Shin, C. T. (1982). High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method. J. Comput. Physics, 48, 387- 411.
[3] 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 Transfer, 35(8), 1881- 1892.
[4] Hakan, F., & Oztop, I. D. (2004). Mixed convection in two-sided lid driven differentially heated square cavity. Int. J. Heat Mass Transfer, 47, 1761-1769.
[5] Chamkha, A. J. (2002). Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation or absorption. Numerical Heat Transfer, Part A, 41, 529-546.
[6] Hussain, S. (2017). Effects of inclination angle on mixed convective nanofluid flow in a double lid-driven cavity with discrete heat sources. Int. J. Heat Mass Transfer, 106, 847- 860.
[7] Sivasankaran, V. S. (2013). Numerical study on mixed convection in an inclined lid-driven cavity with discrete heating. Int. Comm. Heat Mass Transfer, 46, 112- 125.
[8] Sharif, M. A. R. (2007). Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom, Appl. Therm. Eng, 27, 1036-1042.
[9] Cheng, T. S. (2011). Characteristics of mixed convection heat transfer in a lid-driven square cavity with various Richardson and Prandtl numbers. Int. J. Thermal Sciences, 50, 197- 205.
[10] Sousa, S. K. (2014). A detailed study of lid-driven cavity flow at moderate Reynolds numbers using Incompressible SPH. Int. J. Num. Methods Fluids, 76, 653- 668.
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[14] Ghia, U., Ghia, K. N., & Shin, C. T. (1982). High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method. J. Comput. Phys., 48, 387–411.
[15] Cao, Z., & Esmail, M. N. (1995). Numerical study on hydrodynamics of short-dwell paper coaters, AIChE J., 41, 1833–1842.
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[18] Hellebrand, H. Tape Casting, in: R. J. Brook (Ed.), Processing of Ceramics, Part1, VCH Verlagsgesellschaft mbH, 17A, Weinheim, 1996, 190–265.
[19] Leong, C. W., & Ottino, J. M. (1989). Experiments on mixing due to chaotic advection in a cavity. J. Fluid Mech., 209, 463–499.
[20] Alleborn, N., Raszillier, H., &Durst, F. (1999). Lid-driven cavity with heat and mass transport. Int. J. Heat Mass Trans., 42, 833–853.
[21] Pal, D. R., Saha, G., & Saha, K. C. (2018). A case study of double lid driven cavity for low Reynolds number flow. Dhaka University J. Science, 66(2), 95-101.
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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

    Kajal Chandra Saha, Goutam Saha, Doli Rani Pal. (2018). Double Lid Driven Cavity with Different Moving Wall Directions for Low Reynolds Number Flow. International Journal of Applied Mathematics and Theoretical Physics, 4(3), 67-72. https://doi.org/10.11648/j.ijamtp.20180403.11

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    ACS Style

    Kajal Chandra Saha; Goutam Saha; Doli Rani Pal. Double Lid Driven Cavity with Different Moving Wall Directions for Low Reynolds Number Flow. Int. J. Appl. Math. Theor. Phys. 2018, 4(3), 67-72. doi: 10.11648/j.ijamtp.20180403.11

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    AMA Style

    Kajal Chandra Saha, Goutam Saha, Doli Rani Pal. Double Lid Driven Cavity with Different Moving Wall Directions for Low Reynolds Number Flow. Int J Appl Math Theor Phys. 2018;4(3):67-72. doi: 10.11648/j.ijamtp.20180403.11

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  • @article{10.11648/j.ijamtp.20180403.11,
      author = {Kajal Chandra Saha and Goutam Saha and Doli Rani Pal},
      title = {Double Lid Driven Cavity with Different Moving Wall Directions for Low Reynolds Number Flow},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {4},
      number = {3},
      pages = {67-72},
      doi = {10.11648/j.ijamtp.20180403.11},
      url = {https://doi.org/10.11648/j.ijamtp.20180403.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijamtp.20180403.11},
      abstract = {In this paper, a numerical examination used to analyze the flow and heat transfer characteristics inside a double lid-driven cavity underneath buoyancy consequences of thermal diffusion. The lid is due to the movement of the isothermal vertical sidewalls of different constant temperatures, while other walls are kept adiabatic. Also, the upright walls are moving at a constant rate and four different moving wall directions are considered along these walls. Further, the governing equations of the flow and thermal fields are transformed into dimensionless equations and then solved numerically using finite difference method. A contrast of the current learn is additionally carried out with the formerly published works and observed excellent agreement. Moreover, the results from numerical simulations have been presented in the form of velocities and isothermal profiles, shown graphically and discussed for different Reynolds number. Result unveils that, the influence of the development of the velocity profiles in the chamber decreases with the augmentation of Re. Besides, the intensification of Reynolds number ends in forming diminution of thermal boundary layers near the heated wall. In addition, the maximum Average Nusselt number can be obtained when the left lid poignant towards positive direction and the right lid poignant to the same direction.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Double Lid Driven Cavity with Different Moving Wall Directions for Low Reynolds Number Flow
    AU  - Kajal Chandra Saha
    AU  - Goutam Saha
    AU  - Doli Rani Pal
    Y1  - 2018/10/15
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ijamtp.20180403.11
    DO  - 10.11648/j.ijamtp.20180403.11
    T2  - International Journal of Applied Mathematics and Theoretical Physics
    JF  - International Journal of Applied Mathematics and Theoretical Physics
    JO  - International Journal of Applied Mathematics and Theoretical Physics
    SP  - 67
    EP  - 72
    PB  - Science Publishing Group
    SN  - 2575-5927
    UR  - https://doi.org/10.11648/j.ijamtp.20180403.11
    AB  - In this paper, a numerical examination used to analyze the flow and heat transfer characteristics inside a double lid-driven cavity underneath buoyancy consequences of thermal diffusion. The lid is due to the movement of the isothermal vertical sidewalls of different constant temperatures, while other walls are kept adiabatic. Also, the upright walls are moving at a constant rate and four different moving wall directions are considered along these walls. Further, the governing equations of the flow and thermal fields are transformed into dimensionless equations and then solved numerically using finite difference method. A contrast of the current learn is additionally carried out with the formerly published works and observed excellent agreement. Moreover, the results from numerical simulations have been presented in the form of velocities and isothermal profiles, shown graphically and discussed for different Reynolds number. Result unveils that, the influence of the development of the velocity profiles in the chamber decreases with the augmentation of Re. Besides, the intensification of Reynolds number ends in forming diminution of thermal boundary layers near the heated wall. In addition, the maximum Average Nusselt number can be obtained when the left lid poignant towards positive direction and the right lid poignant to the same direction.
    VL  - 4
    IS  - 3
    ER  - 

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