Effect of volumetric radiation on natural convection in a cavity with a horizontal fin using the lattice Boltzmann method

  • Hashem Ahmadi Tighchi
  • Masoud Sobhani
  • Javad Abolfazli Esfahani
Regular Article
  • 12 Downloads

Abstract.

The lattice Boltzmann method (LBM) is presented for the effects of volumetric radiation on laminar natural convection in a square cavity with a horizontal fin on the hot wall containing an absorbing, emitting and scattering medium. Accordingly, the flow, energy and radiative equations are solved by separate distribution functions in the LBM. A parametric study is performed: the effects of Rayleigh number and radiative parameters, such as extinction coefficient and scattering albedo on the flow and temperature fields are investigated. It is found that the isotherms become dense near the cold wall, due to highly participating properties and Rayleigh number. Also, the Nusselt number ratio (NNR) on the clod wall is examined for values of fin length and height. The maximum NNR is found at the longest fin length and near top wall for a given Rayleigh number.

References

  1. 1.
    A. Yücel, S. Acharya, M. Williams, Numer. Heat Transf. Part A 15, 2 (1989)CrossRefGoogle Scholar
  2. 2.
    C. Balaji, S. Venkateshan, Int. J. Heat Fluid Flow 16, 2 (1995)CrossRefGoogle Scholar
  3. 3.
    B. Mondal, S.C. Mishra, Numer. Heat Transf. Part A 55, 1 (2008)CrossRefGoogle Scholar
  4. 4.
    F. Moufekkir, M.A. Moussaoui, A. Mezrhab, H. Naji, D. Lemonnier, J. Quant. Spectrosc. Radiat. Transf. 113, 13 (2012)CrossRefGoogle Scholar
  5. 5.
    T. Hayat, S. Qayyum, B. Ahmad, M. Waqas, Eur. Phys. J. Plus 131, 12 (2016)CrossRefGoogle Scholar
  6. 6.
    K. Milani Shirvan, M. Mamourian, S. Mirzakhanlari, A.B. Rahimi, R. Ellahi, Int. J. Numer. Methods Heat Fluid Flow 27, 10 (2017)Google Scholar
  7. 7.
    R. Scozia, R.n.L. Frederick, Numer. Heat Transf. Part A 20, 2 (1991)CrossRefGoogle Scholar
  8. 8.
    A. Zeeshan, R. Ellahi, M. Hassan, Eur. Phys. J. Plus 129, 261 (2014)CrossRefGoogle Scholar
  9. 9.
    M. Sheikholeslami, R. Ellahi, C. Fetecau, Math. Prob. Eng. 2017, 5830279 (2017)CrossRefGoogle Scholar
  10. 10.
    K. Milani Shirvan, R. Ellahi, M. Mamourian, M. Moghiman, Int. J. Heat Mass Transfer 107, 1110 (2017)CrossRefGoogle Scholar
  11. 11.
    X. Shi, J. Khodadadi, J. Heat Transf. 125, 4 (2003)Google Scholar
  12. 12.
    S.H. Tasnim, M.R. Collins, Int. Commun. Heat Mass Transf. 31, 5 (2004)Google Scholar
  13. 13.
    E. Bilgen, Int. J. Heat Mass Transfer 48, 17 (2005)Google Scholar
  14. 14.
    A. Da Silva, L. Gosselin, Int. J. Therm. Sci. 44, 6 (2005)CrossRefGoogle Scholar
  15. 15.
    A. Ben-Nakhi, A.J. Chamkha, Int. J. Therm. Sci. 46, 5 (2007)CrossRefGoogle Scholar
  16. 16.
    R.L. Frederick, S.G. Moraga, Int. J. Heat Fluid Flow 28, 2 (2007)CrossRefGoogle Scholar
  17. 17.
    A. Haghighi, K. Vafai, Numer. Heat Transf. Part A 66, 1 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    G. Nardini, M. Paroncini, R. Vitali, Heat Mass Transf. 51, 12 (2015)CrossRefGoogle Scholar
  19. 19.
    A. Elatar, M.A. Teamah, M.A. Hassab, Int. J. Therm. Sci. 99, 41 (2016)CrossRefGoogle Scholar
  20. 20.
    A. Azimifar, S. Payan, Appl. Therm. Eng. 110, 1371 (2017)CrossRefGoogle Scholar
  21. 21.
    S. Saravanan, C. Sivaraj, Int. J. Heat Fluid Flow 40, 54 (2013)CrossRefGoogle Scholar
  22. 22.
    M. Mamourian, K. Milani Shirvan, R. Ellahi, A.B. Rahimi, Int. J. Heat Mass Transfer 102, 544 (2016)CrossRefGoogle Scholar
  23. 23.
    K. Milani Shirvan, M. Mamourian, S. Mirzakhanlari, R. Ellahi, Int. J. Heat Mass Transfer 105, 811 (2017)CrossRefGoogle Scholar
  24. 24.
    K. Milani Shirvan, M. Mamourian, R. Ellahi, Int. J. Numer. Methods Heat Fluid Flow 27, 9 (2017)Google Scholar
  25. 25.
    P. Asinari, S.C. Mishra, R. Borchiellini, Numer. Heat Transf. Part B 57, 2 (2010)CrossRefGoogle Scholar
  26. 26.
    A.F. Di Rienzo, P. Asinari, R. Borchiellini, S.C. Mishra, Int. J. Numer. Methods Heat Fluid Flow 21, 5 (2011)CrossRefGoogle Scholar
  27. 27.
    S.C. Mishra, H. Poonia, R.R. Vernekar, A.K. Das, Heat Transf. Eng. 35, 14 (2014)Google Scholar
  28. 28.
    S.C. Mishra, H. Poonia, A.K. Das, P. Asinari, R. Borchiellini, Numer. Heat Transf. Part A 66, 6 (2014)Google Scholar
  29. 29.
    H.A. Tighchi, J. Esfahani, J. Thermophys. Heat Transf. 31, 3 (2017)Google Scholar
  30. 30.
    Y. Wang, D.K. Sun, Y.L. He, W.Q. Tao, Eur. Phys. J. Plus 130, 9 (2015)ADSCrossRefGoogle Scholar
  31. 31.
    M. Sheikholeslami, R. Ellahi, Z. Naturforsch. A 70, 2 (2015)Google Scholar
  32. 32.
    A.A. Mohamad, Lattice Boltzmann method: fundamentals and engineering applications with computer codes, 1st ed. (Springer, London, Verlag, 2011)Google Scholar
  33. 33.
    S. Succi, The lattice Boltzmann method for fluid dynamics and beyond, 1st ed. (Oxford University, England, Oxford, 2001)Google Scholar
  34. 34.
    M. Sukop, D.T. Thorne, Lattice Boltzmann Modeling, 1st ed. (Springer, Berlin, Heidelberg, 2006)Google Scholar
  35. 35.
    B. Mondal, X. Li, Int. J. Heat Mass Transfer 53, 21 (2010)CrossRefGoogle Scholar
  36. 36.
    S.C. Mishra, A. Akhtar, A. Garg, Numer. Heat Transf. Part A 65, 2 (2014)CrossRefGoogle Scholar
  37. 37.
    P.L. Bhatnagar, E.P. Gross, M. Krook, Phys. Rev. 94, 3 (1954)CrossRefGoogle Scholar
  38. 38.
    H. Dixit, V. Babu, Int. J. Heat Mass Transfer 49, 3 (2006)CrossRefGoogle Scholar
  39. 39.
    M.F. Modest, Radiative heat transfer, 3rd ed. (Academic Press, 2006)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringFerdowsi University of MashhadMashhadIran

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