Numerical study of the Boussinesq approach validity for natural convection and surface thermal radiation in an open cavity

M. Montiel González^a, J. Hinojosa Palafox^b, and C. Estrada Gasca^a

^a Institute of Renewable Energies, Universidad Nacional Autónoma de México, Apartado Postal 34, Temixco, 62580, Morelos, Mexico, Tel. +52 (55) 56229744 e-mail: cestrada@cie.unam.mx

^b Departament of Chemical Engineering and Metallurgy, University of Sonora, Blvd. Luis Encinas y Rosales s/n, Hermosillo, 83000, Sonora, México, Tel. +52 (662) 2592106 e-mail: fhinojosa@iq.uson.mx

Abstract

In this work the validity of the Boussinesq approach for the heat transfer calculations in an open cavity considering natural convection and surface thermal radiation is studied. Numerical calculations were conducted for Rayleigh number (Ra) values in the range of 10⁴ -10⁶. The temperature difference between the hot wall and the bulk fluid (ΔT) was varied between 10 and 100 K, and was represented as a dimensionless temperature difference (φ). The deviations for the temperature fields and fluid flow patterns, between variable properties and Boussinesq approach are noticeable for φ=0.333. For total Nusselt numbers, the results with Boussinesq approach and variable properties, indicates deviations within 0.22 % (Ra=10⁵ and φ=0.033) and 5 % (Ra=10⁴ and φ=0.333).

Keywords: Boussinesq approach; natural convection; thermal radiation; open cavity.

PACS: 44.25.+f, 44.40.+a

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References

1. P. Le Quere, J.A. Humphrey, and F.S. Sherman, Numerical Heat Transfer 4 (1981) 249-283.         [ Links ]

2. F. Penot, Numerical Heat Transfer 5 (1982) 421-437.         [ Links ]

3. J.A. Humphrey, and W.M. To, Free and mixed convection in a heated cavity, International Journal of Heat and Mass Transfer 29 (1986) 593-610.         [ Links ]

4. D. Angirasa, J.G. Eggels, and F.T. Nieuwstadt, Numerical Heat Transfer Part A 28 (1995) 755-768.         [ Links ]

5. S.K.S. Boetcher and E. M. Sparrow, International Journal of Heat and Mass Transfer 52 (2009) 3850-3856.         [ Links ]

6. J. F. Hinojosa, and J. Cervantes de Gortari, Heat and Mass Transfer 46 (2010) 595-606.         [ Links ]

7. Y.L. Chan, and C.L. Tien, Numerical Heat Transfer 8 (1985) 65-80.         [ Links ]

8. Y.L. Chan, and C.L. Tien, International Journal of Heat and Mass Transfer 28 (1985) 603-612.         [ Links ]

9. D. Angirasa, M.J. Pourquie, and F.T. Nieuwstadt, Numerical Heat Transfer Part A 22 (1992) 223-239.         [ Links ]

10. A.A. Mohamad, Numerical Heat Transfer Part A 27 (1995) 705-716.         [ Links ]

11. I. Sezai and A.A. Mohamad, International Journal of Numerical Methods for Heat and Fluid Flow 8 (1998) 800-813.         [ Links ]

12. O. Polat, and E. Bilgen, International Journal of Thermal Sciences 41 (2002) 360-368.         [ Links ]

13. J.F. Hinojosa, G. Alvarez, C.A. Estrada, Rev. Mex. Fis. 52 (2006) 111-119.         [ Links ]

14. A.A. Mohamad, M. El-Ganaoui, and R. Bennacer, International Journal of Thermal Sciences 48 (2009) 1870-1875.         [ Links ]

15. M.A. Hossain, S. Asghar, and R.S.R. Gorla, International Journal of Numerical Methods for Heat and Fluid Flow 20 (2010) 759-772.         [ Links ]

16. J.O. Juarez, J.F. Hinojosa, J.P. Xaman, and M. Perez, International Journal of Thermal Sciences 50 (2011)2184-2197.         [ Links ]

17. J.L. Lage, J.S. Lim, and A. Bejan, Journal of Heat Transfer 114 (1992) 479-486.         [ Links ]

18. C. Balaji and S.P. Venkateshan, International Journal of Heat and Fluid Flow 15 (1994) 317-324.         [ Links ]

19. C. Balaji and S.P. Venkateshan, International Journal of Heat and Fluid Flow 16 (1995) 139-144.         [ Links ]

20. S.N. Singh and S.P. Venkateshan, International Journal of Thermal Sciences 43 (2004) 865-876.         [ Links ]

21. J.F. Hinojosa, R.E. Cabanillas, G. Alvarez, and C.A. Estrada, International Communications for Heat and Mass Transfer 32 (2005) 1184-1192.         [ Links ]

22. J.F. Hinojosa, R.E. Cabanillas, G. Alvarez, and C.A. Estrada, Numerical Heat Transfer Part A 48 (2005) 179-196.         [ Links ]

23. H. Nouaneguea, A. Muftuoglu, and E. Bilgen, International Journal of Heat and Mass Transfer 51 (2008) 6054-6062.         [ Links ]

24. J. F. Hinojosa Palafox, Rev. Mex. Fis. 58 (2012) 19-28.         [ Links ]

25. M. Yang, L. Li and Y. Zhang, Journal of Heat Transfer 134 (2012) 09450.         [ Links ]

26. O. Polat and E. Bilgen, International Journal of Heat and Mass Transfer 46 (2003) 1563-1573.         [ Links ]

27. A. Koca, International Communications in Heat and Mass Transfer 35 (2008) 1385-1395.         [ Links ]

28. M. Miyamoto, T.H. Kuehn, R.J. Goldstein, and Y. Katoh, Numerical Heat Transfer Part A 15 (1989) 411-430.         [ Links ]

29. A.H. Abib and Y. Jaluria, International Journal of Heat and Mass Transfer 38 (1995) 2489-2500.         [ Links ]

30. E. Bilgen and H. Oztop, International Journal of Heat and Mass Transfer 48 (2005) 1470-1479.         [ Links ]

31. K. Vafai and J. Ettefagh, International Journal of Heat and Mass Transfer 33 (1990) 2311-2328.         [ Links ]

32. K. Vafai and J. Ettefagh, International Journal of Heat and Mass Transfer 33 (1990) 2329-2344.         [ Links ]

33. K. Khanafer and K. Vafai, International Journal of Heat and Mass Transfer 43 (2000) 4087-4100.         [ Links ]

34. K. Khanafer and K. Vafai, International Journal of Heat and Mass Transfer 45 (2002) 2527-2538.         [ Links ]

35. K. Khanafer, K. Vafai, and M. Lighstone, International Journal of Heat and Mass Transfer 45 (2002) 5171-5190.         [ Links ]

36. A. Andreozzi and O. Manca, Numerical Heat Transfer Part A: Applications 57 (2010) 453-472.         [ Links ]

37. D.D. Gray and A. Giorgini, International Journal of Heat and Mass Transfer 19 (1976) 545-551.         [ Links ]

38. Z.Y. Zhong, K.T. Yang, J.R. Lloyd, Journal of Heat Transfer 107 (1985) 183-140.         [ Links ]

39. M. Modest, Radiative Heat Transfer, (McGraw-Hill: New York, USA, 1993).         [ Links ]

40. F. P. Incropera and D. P. de Witt, Fundamentals of Heat and Mass Transfer, Appendix A, (Wiley and sons, Fourth Edition, 1996).         [ Links ]

41. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, (Hemisphere Publishing Corporation, 1980).         [ Links ]

42. H. K. Versteg and W. Malalasekera, An Introduction to Computational Fluid Dynamics. (The Finite Volume Method, Wiley & Sons Inc., 1995).         [ Links ]

43. M. Zedan and G. Schneider, A three-dimensional modified strongly implicit procedure for heat conduction, AIAA 21 (1983) 295-303.         [ Links ]