Nusselt Number for Laminar Flow in Entrance Zone of a Hot Tube

Document Type : Original Article

Authors

Associate Professor, Sirjan University of Technology, Sirjan, Iran

Abstract

Solving many important industrial problems requires knowing the values ​​of the displacement heat transfer coefficient of one or more fluid streams in different equipment, systems or pipes. In this study, a numerical model has been developed to simulate compressible fluid flow at the inlet of a hot pipe with different angles to the horizon. In this area, the hydrodynamic and thermal boundary layers of the fluid flow are developing. Due to the turbulence of fluid flow due to the interaction of heat and fluid flow inside this pipe, three-dimensional turbulent model was used for this simulation. For this purpose, continuity equations, compressible Navier-Stokes, Reynolds stress model, and turbulent and compressible energy equations are solved simultaneously. Then, using a series of numerical runs through the concepts of experimental design and optimization methods, a prediction formula for the Nusselt number for these flows has been obtained. Finally, the ability of this formula has been investigated using a set of laboratory data.

Keywords

Smiley face

References

  1. Smith, J. M. “Introduction to Chemical Engineering Thermodynamics”, New York, Mcgraw Hill Education, 2018.

    1. 2. Kauzmann, W. “Kinetic Theory of Gases”. Courier Corporation, 2012.
    2. 3. Sutherland, W. “The Viscosity of gases and Molecular Force”. Phil. Mag. J. Sci., 36, No. 223, pp. 507-531, 1893. doi: 10.1080/14786449308620508
    3. 4. Shah, R. “Laminar Flow Forced Convection in Ducts”, Supp. Adv. Heat Trans., p 153-195, 1978.
    4. Lee, P. S. and Garimella, S. V. “Thermally Developing Flow and Heat Transfer in Rectangular Microchannels of different aspect ratios”. Int. J. Heat Mass Trans., Vol. 49, No. 17, pp. 3060-3067, 2006.
    5. 6. Smith, A. and Nochetto, H. “Laminar Thermally Developing Flow in Rectangular Channels and Parallel Plates: Uniform Heat Flux”. Heat Mass Trans., Vol. 50, No. 11, pp. 1627-1637, 2014. doi:10.1016/j.csite.2021.100856
    6. 7. Renksizbulut, M. and Niazmand, H. “Laminar Flow and Heat Transfer in the Entrance Region of Trapezoidal Channels with Constant Wall Temperature”. J. Heat Trans., Vol. 128, No. 1, pp. 63-74, 2006 doi:1016/j.ijthermalsci.2005.12.008.
    7. McHale, J. P. and Garimella, S. V. “Heat Transfer in Trapezoidal Microchannels of Various Aspect Ratios”. Int. J.l Heat Mass Trans., Vol. 53, No. 3, pp. 365-375, 2010. doi:10.1016/j.ijheatmasstransfer.2009.09.020
    8. Saha, S. K., Agrawal, A., and Soni, Y.  “Heat Transfer Characterization of Rhombic Microchannel for H1 and H2 Boundary Conditions”. Int. J. Therm. Sci., Vol. 111, pp. 223-233, 2017. DOI: 10.1615/JEnhHeatTransf.2021038523
    9. Maia, C. R. M., Aparecido, J. B., and Milanez, L. “Heat Transfer in Laminar Flow of Non-Newtonian Fluids in Ducts of Elliptical Section”. Int. J. Therm. Sci., Vol. 45, No. 11, pp. 1066-1072, 2006. doi:10.1016/j.ijthermalsci.2006.02.001
    10. Maia, C. R. M., Aparecido, J. B., and Milanez, L. F.  “Thermally Developing Forced Convection of Non-Newtonian Fluids Inside Elliptical Ducts”. Heat Trans. Eng., Vol. 25, No. 7, pp. 13-22, 2004. doi:10.2514/1.T6193
    11. 12. Birken, P. “Numerical Methods for the Unsteady Compressible Navier-Stokes Equations”. Kassel University, 2013.
    12. Launder, B. E., Reece, G. J., and Rodi, W.  “Progress in the Development of a Reynolds-Stress Turbulence Closure”. J. Fluid Mech., Vol. 68, No. 3, pp. 537-566, 1975. doi:10.1017/S0022112075001814
    13. Wilcox, D. C. “Turbulence modeling for CFD”., Vol. 2, DCW industries La Canada, CA, 1998.
    14. 15. Abolpour, B., Afsahi, M. M., Yaghobi,, Soltani Goharrizi, A., and Azizkarimi, M. “Interaction of Heat Transfer and Gas Flow in a Vertical Hot Tube”. Heat Mass Trans., Vol. 53, No. 7, pp. 2409-2417, 2017.
    15. Abolpour, B. and Shamsoddini, R., “A Predictive Formula for the Nusselt Number of Compressible Laminar Fluid Flow Passing the Thermal Developing Zone of a Hot Tube”. Heat Trans. Asian Res., Vol. 48, No. 4, pp. 1529-1543, 2019.

    16. Hausen,H. “Darstellungdes Warmeuberganges in Rohrendurchverallgemeinerte. Potenzbeziehungen”.Z.VDIBeih

                     Verfahrenstech, Vol. 4, No. 91, pp. 91-98, 1943.doi: 10.22059/jcamech.2018.255831.263

      1. 18. Metais, B. and Eckert, “Forced, Mixed, and Free Convection Regimes”. J. Heat Trans., Vol. 86, pp. 295-296, 1964. doi:10.1016/S0017-9310(97)00026-4
      2. Mills, A. F. “Heat Transfer”. Prentice Hall, 1999.
      3. 20. Oliver, D.“Heat Transfer Due to Combined Free and Forced Convection in a Horizontal and Isothermal Tube”. ASME J. Heat Trans., 93, pp. 380–384, 1972.
      4.  Sieder, E. N. and Tate, G. E.  “Heat Transfer and Pressure Drop of Liquids in Tubes”. Ind. Eng. Chem., Vol. 28, No. 12, pp. 1429-1435, 1936. doi:10.1021/ie50324a027

Files

History

  • Receive Date: 25 April 2022
  • Revise Date: 17 October 2022
  • Accept Date: 19 November 2022
  • Publish Date: 02 March 2023

Share

How to cite

Statistics