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Effects of Aspect Ratios on Flow Friction and Thermal Behavior Inside a Close Domain Using Lattice Boltzmann Method

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

Numerical study of flow friction and thermal behavior on a moving lid of a triangular cavity with various aspect ratios has been discussed using a Thermal Lattice Boltzmann Method (TLBM). To analyze the combined force and free convection, known as mixed convection, flows and heat transfer process in a lid driven triangular cavity with various aspect ratios AR(=L/H)=0.5, 1.0 and 2.0 are taken into account in the present study. The results are presented as stream function in terms of velocity, average heat transfer rate in terms of Nusselt number (Nu), and friction on moving lid of cavity for different Reynolds number (Re) as well as buoyancy parameter (λ). The heat transfer rate and friction on moving lid increased and decreased significantly with increasing Reynolds number and aspect ratios but they are linearly and very slowly changed with buoyancy effects. Similarly, the fluid flow behavior significantly changed with higher Reynolds number and aspect ratios compare to lower Re and AR. In addition, the less friction and more heat transfer occurred at case of free convection dominant case compare to forced convection dominant case. Similar behavior is observed for fluid flow analysis inside cavity. The model is validated by other numerical scheme and a very good agreement is found.

Published in American Journal of Applied Mathematics (Volume 3, Issue 1-1)

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

DOI 10.11648/j.ajam.s.2015030101.11
Page(s) 1-7
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), 2014. Published by Science Publishing Group

Keywords

Lattice-Boltzmann, Heat Transfer, Friction Factor, Richardson Number, Reynolds Number, Stream Function

References
[1] C. Sun, B. Yu, H. F. Oztop, Yi. Wnag, and J. Wei, “Control of mixed convection in lid-driven enclosures using conductive triangular fins”, Int. J. Heat and Mass Transfer, Vol. 54, pp. 894-909, 2011.
[2] M. Li, and T. Tang, “Steady viscous flow in a triangular cavity by efficient numerical techniques”, Computers Math. App.,Vol. 31, No.10, pp.55-65, 1996.
[3] M. Ahmed, and H. C. Kuhlmann, “Flow instability in triangular lid-driven cavities with wall motion away from a rectangular corner”, Fluid Dyn. Res., Vol.44, pp.025501-21, 2012.
[4] C-L Chen, and C-H.Cheng, “Numerical study of flow and thermal behavior of lid-driven flows in cavities of small aspect ratios”, Int. J. Num. Methods in Fluid, Vol.52, pp.785-799, 2006.
[5] T. Basak, G. Aravind, and S. Roy, “Visualization of heat flow due to natural convection within triangular cavities using Bejan’s heatline concept”, Int. J. of Heat and Mass Transfer, Vol.52, pp.2824-2833, 2009.
[6] Y. H. Qian, D. D’Humieres, and , P. Lallemand, “Lattice BGK models for Navier- Stokes equation”, Euro physics letter, Vol. 17, No.6, pp. 479-484, 1992.
[7] H. Chen, S. Chen, and W. H. Matthaeus, “Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method”, Physical Review A, Vol. 45, No.8, pp. 5339-5342, 1992.
[8] X. He, S. Chen, and G. D. Doolen, “A novel thermal model for the Lattice Boltzmann method in incompressible limit”, J. Comp. Physics, Vol.146, pp. 282-300, 1988.
[9] M. A. Taher, S. C. Saha, Y. W Lee, and H. D. Kim, “Numerical study of lid driven square cavity with heat generation using LBM”, Americal Journal of Fluid Mechanics, Vol.3, No.2, pp.340-344, 2013.
[10] A. Mohammad, Applied lattice Boltzmann method for Transport phenomena, momentum, heat and mass transfer, The University of Calgary, Albetra, Canada, 2007.
[11] Succi, S., The lattice Boltzmann equation for fluid dynamics and beyond, Oxford University, UK, 2001.
[12] A. R. Darzi, M. Farhadi, K. Sedighi, E. Fattahi, and H. Nemati, “Mixed convection simulation on inclined lid driven cavity using Lattice Boltzmann method”, IJST, Transactions of Mechanical Engineering, Vol. 35, No. M1, pp.73–83, 2011.
[13] M. Jafari, M. Farhadi, K. Sedighi, and E. Fattahi, “Numerical simulation of convection heat transfer in a lid driven cavity with an open side”, World Academy of Science, Engineering and Tecnology, Vol.5, No.11, pp.291-295, 2011.
[14] Z. Guo, and T. S. Zhao, “A Lattice Boltzamnn model for convection heat transfer in porous media”, Numerical Heat Transfer, Part B, Vol.47, pp.157-177, 2005.
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  • APA Style

    M. A. Taher, Litan Kumar Saha, Y. W. Lee. (2014). Effects of Aspect Ratios on Flow Friction and Thermal Behavior Inside a Close Domain Using Lattice Boltzmann Method. American Journal of Applied Mathematics, 3(1-1), 1-7. https://doi.org/10.11648/j.ajam.s.2015030101.11

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    ACS Style

    M. A. Taher; Litan Kumar Saha; Y. W. Lee. Effects of Aspect Ratios on Flow Friction and Thermal Behavior Inside a Close Domain Using Lattice Boltzmann Method. Am. J. Appl. Math. 2014, 3(1-1), 1-7. doi: 10.11648/j.ajam.s.2015030101.11

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    AMA Style

    M. A. Taher, Litan Kumar Saha, Y. W. Lee. Effects of Aspect Ratios on Flow Friction and Thermal Behavior Inside a Close Domain Using Lattice Boltzmann Method. Am J Appl Math. 2014;3(1-1):1-7. doi: 10.11648/j.ajam.s.2015030101.11

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  • @article{10.11648/j.ajam.s.2015030101.11,
      author = {M. A. Taher and Litan Kumar Saha and Y. W. Lee},
      title = {Effects of Aspect Ratios on Flow Friction and Thermal Behavior Inside a Close Domain Using Lattice Boltzmann Method},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {1-1},
      pages = {1-7},
      doi = {10.11648/j.ajam.s.2015030101.11},
      url = {https://doi.org/10.11648/j.ajam.s.2015030101.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030101.11},
      abstract = {Numerical study of flow friction and thermal behavior on a moving lid of a triangular cavity with various aspect ratios has been discussed using a Thermal Lattice Boltzmann Method (TLBM). To analyze the combined force and free convection, known as mixed convection, flows and heat transfer process in a lid driven triangular cavity with various aspect ratios AR(=L/H)=0.5, 1.0 and 2.0 are taken into account in the present study. The results are presented as stream function in terms of velocity, average heat transfer rate in terms of Nusselt number (Nu), and friction on moving lid of cavity for different Reynolds number (Re) as well as buoyancy parameter (λ). The heat transfer rate and friction on moving lid increased and decreased significantly with increasing Reynolds number and aspect ratios but they are linearly and very slowly changed with buoyancy effects. Similarly, the fluid flow behavior significantly changed with higher Reynolds number and aspect ratios compare to lower Re and AR. In addition, the less friction and more heat transfer occurred at case of free convection dominant case compare to forced convection dominant case. Similar behavior is observed for fluid flow analysis inside cavity. The model is validated by other numerical scheme and a very good agreement is found.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - Effects of Aspect Ratios on Flow Friction and Thermal Behavior Inside a Close Domain Using Lattice Boltzmann Method
    AU  - M. A. Taher
    AU  - Litan Kumar Saha
    AU  - Y. W. Lee
    Y1  - 2014/11/29
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ajam.s.2015030101.11
    DO  - 10.11648/j.ajam.s.2015030101.11
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 1
    EP  - 7
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.s.2015030101.11
    AB  - Numerical study of flow friction and thermal behavior on a moving lid of a triangular cavity with various aspect ratios has been discussed using a Thermal Lattice Boltzmann Method (TLBM). To analyze the combined force and free convection, known as mixed convection, flows and heat transfer process in a lid driven triangular cavity with various aspect ratios AR(=L/H)=0.5, 1.0 and 2.0 are taken into account in the present study. The results are presented as stream function in terms of velocity, average heat transfer rate in terms of Nusselt number (Nu), and friction on moving lid of cavity for different Reynolds number (Re) as well as buoyancy parameter (λ). The heat transfer rate and friction on moving lid increased and decreased significantly with increasing Reynolds number and aspect ratios but they are linearly and very slowly changed with buoyancy effects. Similarly, the fluid flow behavior significantly changed with higher Reynolds number and aspect ratios compare to lower Re and AR. In addition, the less friction and more heat transfer occurred at case of free convection dominant case compare to forced convection dominant case. Similar behavior is observed for fluid flow analysis inside cavity. The model is validated by other numerical scheme and a very good agreement is found.
    VL  - 3
    IS  - 1-1
    ER  - 

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Author Information
  • Dept. of Mechanical and Automotive Engineering, Pukyong National University, Busan 608-739, Korea

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

  • Dept. of Mechanical and Automotive Engineering, Pukyong National University, Busan 608-739, Korea

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