Multiple solutions for flow mode−transition in an inclined cavity generated by natural convection

  • Miloud Zellouf Laboratoire de Génie Energétique et Matériaux (LGEM), Université de Biskra, B.P. 145 R.P. 07000, Biskra
  • Noureddine Moummi Laboratoire de Génie Mécanique (LGM) Université de Biskra B.P. 145 R.P. 07000, Biskra
  • Adnane Labed Laboratoire de Génie Mécanique (LGM) Université de Biskra B.P. 145 R.P. 07000, Biskra
  • Kamel Aoues Laboratoire de Génie Energétique et Matériaux (LGEM), Université de Biskra, B.P. 145 R.P. 07000, Biskra

Abstract

An investigation of natural convection in a rectangular cavity (AR = 4) filled with air (Pr = 0.71) heated from the side with adiabatic horizontal walls is carried out numerically. To describe the flow regime, we propose a description of the influence of the angle of inclination and Rayleigh number on the flow patterns likely to develop in this configuration. The numerical analysis of the governing equations of the problem is based on finite volume method with non-staggered grids arrangement and is solved through the iterative SIMPLEC algorithm. Results indicate that the angle of inclination has a significant effect on flow mode transition. The existence of multi-steady solutions closely depends on the value of the Rayleigh number. For that the Hysteresis phenomenon (multi−steady solutions) for Ra ≥ 2000 are demonstrated and parameter maps of Ra vs. φ are proposed.

References

Aoues, K., A. Labed, M. Zellouf, N. Moummi (2007) Convection with double diffusion in a rectangular cavity agitated by parallel gradients, Int. Conference on Modelling and Simulation, Algiers.
Aoues, K., N. Moummi, M. Zellouf, A. Benchabane (2011) Thermal performance improvement of solar air flat plate collector: a theoretical analysis and an experimental study in Biskra, Algeria. International Journal of Ambient Energy 32(2): 95–102.
Arnold, J.N., I. Catton, D.K. Edwards (1976) Experimental investigation of natural convection in inclined rectangular regions of differing aspect ratios. Journal of Heat Transfer 98(1): 67–71.
Bodenshatz, E., W. Pesh, G. Ahlers (2000) Recent developments in Rayleigh-Bénard convection. Annual review of fluid mechanics 32(1): 709–778.
Boussinesq, J. (1903) Théorie Analytique de la Chaleur. Vol. 2, Gauthier-Villars, Paris.
Catton, I. (1978) Natural convection in enclosures. Proceedings of the sixth international heat transfer conference, Vol. 6, pp. 13-31.
Chang, B.H. (2014) Numerical study of flow and heat transfer in differentially heated enclosures. Thermal Science 18(2): 451-463.
Corcione, M. (2003) Effect of thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from below and cooled from above. International Journal of Thermal Sciences 42(2): 199-208.
Elsherbiny, S.M., G.D. Raithby, K.G.T. Hollands (1982) Heat transfer by natural convection across vertical and inclined air layers. Journal of Heat Transfer 104(1): 96-102.
Elsherbiny, S.M (1996) Free convection in inclined air layers heated from above. International journal of heat and mass transfer 39(18): 3925-3930.
Hamady, F.J., J.R. Lloyd, H.Q. Yang, K.T. Yang (1989) Study of local natural convection heat transfer in an inclined enclosure. International Journal of Heat and Mass Transfer 32(9): 1697-1708.
Hart, E.J. (1971) Stability of the flow in differentially heated inclined box. Journal of Fluid Mechanics 47(3): 547-576.
Hollands, K.G.T., L. Konicek (1973) Experimental study of the stability of differentially heated inclined air layers. International Journal of Heat and Mass Transfer 16(7): 1467-1476.
Huppert, H.E., J.S. Turner (1981) Double-diffusive convection. Journal of Fluid Mechanics 106: 299-329.
Jaluria, Y. (1980) Natural Convection Heat and Mass Transfer, Oxford, Pergamon Press.
Khezzar, L., D. Siginer, I. Vinogradov (2012) Natural convection in inclined two dimensional rectangular cavities. Heat and Mass Transfer 48(2): 227-239.
Labed, A., A. Aliouali, K. Aoues, M. Zellouf (2005) Etude numérique de la convection naturelle thermosolutale bidimensionnelle dans une enceinte fermée, Journées d’Etudes Nationale de La Mécanique, Ouargla.
Labed, A., N. Moummi, A. Benchabane, K. Aoues, A. Moummi (2012) Performance investigation of single-and double-pass solar air heaters through the use of various fin geometries. International Journal of Sustainable Energy 31(6): 423-434.
Labed, A., N. Moummi, K. Aoues, M. Zellouf (2013) Etude expérimentale des performances thermiques et des pertes de charges de différentes configurations de capteurs solaires plans à air, 16ème Edition des Journées Internationales de Thermique, Marrakech.
Labed, A., N. Moummi, M. Zellouf, K. Aoues, A. Rouag (2014) Effect of different parameters on the solar drying of henna; experimental investigation in the region of Biskra (Algeria). 13th Int. conference on clean energy, Istanbul.
Labed, A., A. Rouag, A. Benchabane, N. Moummi, M. Zerouali (2015) Applicability of solar desiccant cooling systems in Algerian Sahara: Experimental investigation of flat plate collectors. Journal of Applied Engineering Science & Technology, 1 (2): 61-69.
Moummi, N., S. Youcef-Ali, A. Moummi, J.Y. Desmons (2004) Energy analysis of a solar air collector with rows of fins. Renewable Energy 29(13) 2053,2064.
Moummi, N., A. Moummi, K. Aoues, C. Mahboub, S. Youcef-Ali (2010) Systematic forecasts of solar collector’s performance in various sites of different climates in Algeria. International journal of sustainable energy 29(3): 142–150.
Oberbeck, A. (1879) Über die, Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge von Temperatur- differenzen. Annalen der Physik 243(6), 271-292.
Ostrach, S. (1972) Natural convection in enclosures. Advances in heat transfer 8, 161-227.
Ozoe, H., H. Sayama, S.W. Churchill (1975) Natural convection in an inclined rectangular channel at various aspect ratios and angles – experimental measurements. International Journal of Heat and Mass Transfer 18(12): 1425-1431.
Patankar, S.V., D.B. Spalding (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International journal of heat and mass transfer 15(10): 1787-1806.
Patankar, S.V. (1980) Numerical heat transfer and fluid flow. McGraw-Hill, New York.
Soong, C.Y., P.Y. Tzeng, D.C. chiang, T.S. Sheu (1996) Numerical study on mode-transition of natural convection in differentially heated inclined enclosures. International Journal of Heat and Mass Transfer 39(14): 2869-2882.
Turner, J.S. (1985) Multicomponent convection. Annual Review of Fluid Mechanics 17(1): 11-44.
Van Doormaal, J.P., G.D. Raithby (1984) Enhancement of the simple method for predicting incompressible fluid flow. Numerical heat transfer 7(2): 147-163.
Wang, H., M.S. Hamed (2006) Flow mode-transition of natural convection in inclined rectangular enclosures subjected to bidirectional temperature gradients. International journal of thermal sciences 45(8): 782-795.
Zellouf, M., N. Moummi, K. Aoues, A. Labed (2014) Numerical study on heat transfer and flow mode-transition of natural convection in inclined cavity. Proceedings of 2nd Int. Conference on Applied Energetic and Pollution, Constantine, Vol. 2, pp. 524-532.
Zeytounian, R.K. (2003) Joseph Boussinesq and his approximation: a contemporary view. Comptes Rendus Mecanique 331(8): 575-586.
JAEST: Volume 2, Issue 2, December 2016
Published
2016-12-20
How to Cite
ZELLOUF, Miloud et al. Multiple solutions for flow mode−transition in an inclined cavity generated by natural convection. Journal of Applied Engineering Science & Technology, [S.l.], v. 2, n. 2, p. 75-85, dec. 2016. ISSN 2571-9815. Available at: <https://revues.univ-biskra.dz/index.php/jaest/article/view/1893>. Date accessed: 19 apr. 2024.
Citation Formats
Issue
Vol 2 No 2 (2016)
Section
Section B: Thermal, Mechanical and Materials Engineering

Keywords

Natural convection; Inclined cavity; Hysteresis phenomenon; Flow mode transition; Sizing calculations

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