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Mixed Convection Heat Transfer in a Lid Driven Cavity with Wavy Bottom Surface

Received: 22 December 2013     Published: 30 January 2014
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Abstract

The present numerical study is devoted to investigate the mixed convection flow and heat transfer in a lid-driven cavity with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no slip. The cavity vertical walls are insulated while the upper surface is maintained at a uniform temperature higher than the wavy bottom surface. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), the Grshof number (Gr) and the number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail. It is found that these parameters have significant effect on the flow fields; temperature distributions and heat transfer in the cavity. Furthermore, the trend of skin friction and Nusselt number for different values of the aforementioned parameters are presented in this investigation.

Published in American Journal of Applied Mathematics (Volume 1, Issue 5)
DOI 10.11648/j.ajam.20130105.11
Page(s) 92-101
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

Mixed Convection, Wavy Surface, Lid Driven Cavity, Heat Transfer, Numerical Study

References
[1] C. K. Cha, Y. Jaluria, "Recirculating mixed convection flow for energy extraction", Int. J. Heat Mass Transfer, (1984), 27, pp-1801-1810.
[2] L.A.B. Pilkington, "Review lecture, The Float Glass Process", third edition: Proc. R. Soc. Lon., (1969), 314, pp-1-25.
[3] J. Imberger, P.F. Hamblin, "Dynamics of lakes, reservoirs, and cooling ponds", Adv. Rev. Fluid Mech, (1982), 14, pp-153-187.
[4] A.K. Prasad, J.R. Koseff, Combined forced and natural convection heat transfer in a deep lid-driven cavity flow, Int. J. Heat Fluid Flow, (1996), 17, pp 460–467.
[5] P.K. Das, S. Mahmud, "Numerical investigation of natural convection inside a wavy enclosure", Int. J. Therm. Sci, (2003), 42, pp-397-406.
[6] L. Adjlout, O. Imine, A. Azzi, M. Belkadi, "Laminar natural convection in an inclined cavity with a wavy-wall", Int. J. Heat Mass Transfer, (2002), 45, pp-2141-2152.
[7] B.V.R. Kumar, "A study of free convection induced by a vertical wavy surface with heat flux in a porous enclosure", Num. Heat Transfer,Part A (2000), 37, pp-493-510.
[8] K. Khanafer, B. Al-Azmi, Alia Marafie, I. Pop, Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure, Int. J. Heat Mass Transfer, (2009), 52, pp. 1887–1896.
[9] A. M. Al-Amiri, K.M. Khanafer, I. Pop, Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid driven cavity, Int. J. Heat Mass Transfer, (2007), 50, pp. 1771–1780
[10] C. Taylor, P. Hood, A numerical solution of the Navier–Stokes equations using finite element technique, Computers & Fluids 1 (1) (1973) 73–89.
[11] P. Dechaumphai, Finite Element Method in Engineering, 2nd ed. Chulalongkorn University Press, Bangkok, 1999.
[12] R. Iwatsu, J. M. Hyun, K. Kuwahara, "Mixed convection in a driven cavity with a stable vertical temperature gradient", Int. J. Heat Mass Trsmfer, (1993), 36(6), pp-1601-1608.
[13] M. A. H. Mamun, T. R. Tanim, M. M. Rahman, R. Saidur and Shuichi Nagata, "Analysis of Mixed Convection in a Lid Driven Trapezoidal Cavity".
Cite This Article
  • APA Style

    Litan Kumar Saha, Monotos Chandra Somadder, K. M. Salah Uddin. (2014). Mixed Convection Heat Transfer in a Lid Driven Cavity with Wavy Bottom Surface. American Journal of Applied Mathematics, 1(5), 92-101. https://doi.org/10.11648/j.ajam.20130105.11

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    ACS Style

    Litan Kumar Saha; Monotos Chandra Somadder; K. M. Salah Uddin. Mixed Convection Heat Transfer in a Lid Driven Cavity with Wavy Bottom Surface. Am. J. Appl. Math. 2014, 1(5), 92-101. doi: 10.11648/j.ajam.20130105.11

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    AMA Style

    Litan Kumar Saha, Monotos Chandra Somadder, K. M. Salah Uddin. Mixed Convection Heat Transfer in a Lid Driven Cavity with Wavy Bottom Surface. Am J Appl Math. 2014;1(5):92-101. doi: 10.11648/j.ajam.20130105.11

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  • @article{10.11648/j.ajam.20130105.11,
      author = {Litan Kumar Saha and Monotos Chandra Somadder and K. M. Salah Uddin},
      title = {Mixed Convection Heat Transfer in a Lid Driven Cavity with Wavy Bottom Surface},
      journal = {American Journal of Applied Mathematics},
      volume = {1},
      number = {5},
      pages = {92-101},
      doi = {10.11648/j.ajam.20130105.11},
      url = {https://doi.org/10.11648/j.ajam.20130105.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20130105.11},
      abstract = {The present numerical study is devoted to investigate the mixed convection flow and heat transfer in a lid-driven cavity with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no slip. The cavity vertical walls are insulated while the upper surface is maintained at a uniform temperature higher than the wavy bottom surface. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), the Grshof number (Gr) and the number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail. It is found that these parameters have significant effect on the flow fields; temperature distributions and heat transfer in the cavity. Furthermore, the trend of skin friction and Nusselt number for different values of the aforementioned parameters are presented in this investigation.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - Mixed Convection Heat Transfer in a Lid Driven Cavity with Wavy Bottom Surface
    AU  - Litan Kumar Saha
    AU  - Monotos Chandra Somadder
    AU  - K. M. Salah Uddin
    Y1  - 2014/01/30
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ajam.20130105.11
    DO  - 10.11648/j.ajam.20130105.11
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 92
    EP  - 101
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20130105.11
    AB  - The present numerical study is devoted to investigate the mixed convection flow and heat transfer in a lid-driven cavity with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no slip. The cavity vertical walls are insulated while the upper surface is maintained at a uniform temperature higher than the wavy bottom surface. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), the Grshof number (Gr) and the number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail. It is found that these parameters have significant effect on the flow fields; temperature distributions and heat transfer in the cavity. Furthermore, the trend of skin friction and Nusselt number for different values of the aforementioned parameters are presented in this investigation.
    VL  - 1
    IS  - 5
    ER  - 

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

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

  • Department of Management Information Systems, University of Dhaka, Dhaka, Bangladesh

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