A Galerkin Method Solution of Heat Transfer Problems in Closed Channels: Fluid Flow Analysis

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 37)


A heat transfer model of fluid flow inside closed channels with arbitrary shapes has been built from momentum and energy equations. The model equations have been solved with Galerkin-based method. Detailed velocity and temperature fields in the fluid flow have been obtained. Using the solution fields the friction factors and heat transfer rates have been also calculated. To validate the developed solution procedure, the results have been compared to the results of numerical methods and experimental data.


Reynolds Number Basis Function Velocity Profile Wall Shear Stress Skin Friction 
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I thank all reviewers and contributors for their valuable suggestions, comments, and correction in the final version of my manuscript. They were able to constructively pinpoint relevant issues that need to be revised in my manuscript and which will strengthen and improve my paper.


  1. 1.
    Beck, J.V., Cole, K.D., Haji-Sheikh, A., Litkouhi, B.: Heat Conduction Using Green’s Functions,  Chapter 11. Hemisphere Publishing, Washington, D.C. (1992)
  2. 2.
    Gnielinski, V.: New equations for heat and mass transfer in turbulent pipe and channel flow. Int. Chem. Eng. 16, 359–468 (1976)Google Scholar
  3. 3.
    Ghariban, N.: Turbulent flow and heat transfer in ducts. PhD. Thesis, Department of Mechanical Engineering, The University of Texas at Arlington (1993)Google Scholar
  4. 4.
    Haji-Sheikh, A., Mashena, M., Haji-Sheikh, M.J.: Heat transfer coefficient in ducts with constant wall temperature. J. Heat Tran. 105, 878–883 (1983)CrossRefGoogle Scholar
  5. 5.
    Kakac, S., Shah, R., Aung, W.: Handbook of Single-Phase Convective Heat Transfer,  Chapter 2. Wiley, New York (1987)
  6. 6.
    Kantorovitch, L.V., Krylov, V.I.: Approximate Methods of Higher Analysis. Wiley, New York (1960)Google Scholar
  7. 7.
    Laufer, J.: The structure of turbulence in fully developed pipe flow. NACA Rept. 1174 (1954)Google Scholar
  8. 8.
    Malhotra, A., Kang, S.S.: Turbulent prandtl number in circular pipes. Int. J. Heat Mass Tran. 27(8), 2158–2161 (1984)CrossRefGoogle Scholar
  9. 9.
    Nikuradse, J.: Gesetzmabigkiten der turbulenten stromung in glatten Rohen. Forsch. Arb. Ing.-Wes. 356 (1932); English transl., NASA TT F-10, 359 (1966)Google Scholar
  10. 10.
    Richman, J.W., Azad, R.S.: Developing turbulent flow in smooth pipes. Appl. Sci. Res. 28, 419–440 (1973)MATHGoogle Scholar
  11. 11.
    Van Driest, E.R.: On turbulent flow near a wall. J. Aeronaut. Sci. 23, 1007–1012 (1956)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of EngineeringVirginia State UniversityPetersburgUSA

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