Exact Solution of the Two-Dimensional Problem on an Impact Ideal-Liquid Jet

  • V. D. Belik

The two-dimensional problem on the collision of a potential ideal-liquid jet, outflowing from a reservoir through a nozzle, with an infinite plane obstacle was considered for the case where the distance between the nozzle exit section and the obstacle is finite. An exact solution of this problem has been found using methods of the complex-variable function theory. Simple analytical expressions for the complex velocity of the liquid, its flow rate, and the force of action of the jet on the obstacle have been obtained. The velocity distributions of the liquid at the nozzle exit section, in the region of spreading of the jet, and at the obstacle have been constructed for different distances between the nozzle exit section and the obstacle. Analytical expressions for the thickness of the boundary layer and the Nusselt number at the point of stagnation of the jet have been obtained. A number of distributions of the local friction coefficient and the Nusselt number of the indicated jet are presented.


impact jet obstacle exact solution two-dimensional problem boundary layer friction coefficient Nusselt number 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. H. Beitelmal, A. J. Shah, and M. A. Saad, Analysis of an impinging two dimensional jet, J. Heat Transf., 128, 307–310 (2006).Google Scholar
  2. 2.
    D. J. Phares, G. T. Smedley, and R. C. Flagan, The inviscid impingement of a jet with arbitrary velocity profile, Phys. Fluids, 12, No. 8, 2046−2055 (2000).CrossRefzbMATHGoogle Scholar
  3. 3.
    A. Chatterjee and L. J. Deviprasath, Heat transfer in confined laminar axisymmetric impinging jets at small nozzleplate distances: the role of upstream vorticity diffusion, Numer. Heat Transf., Part A: Applications, 39, No. 8, 777−800 (2001).Google Scholar
  4. 4.
    K. S. Choo and S. J. Kim, Heat transfer characteristics of impinging air jets under a fixed pumping power condition, Int. J. Heat Mass Transf., 52, 3169−3175 (2009).MathSciNetCrossRefGoogle Scholar
  5. 5.
    M. T. Scholtz and O. Trass, Transfer in a nonuniform impinging jet. Part II: Boundary layer flow, AIChE J., 16, 90−96 (1970).Google Scholar
  6. 6.
    D. Lytle and B. W. Webb, Air jet impingement heat transfer at low nozzle plate spacings, Int. J. Heat Mass Transf., 37, 1687−1697 (1994).CrossRefGoogle Scholar
  7. 7.
    J. M. Robertson, Hydrodynamics in Theory and Application, Prentice-Hall, New Jersey (1965).Google Scholar
  8. 8.
    L. G. Loitsyanskii, Mechanics of Liquids and Gas [in Russian], Nauka, Moscow (1978).Google Scholar
  9. 9.
    M. A. Lavrentiev and B. V. Shabat, Methods of Complex-Variable Function Theory [in Russian], Nauka, Moscow (1965).Google Scholar
  10. 10.
    L. D. Landau and E. M. Lifshits, Hydrodynamics [in Russian], Nauka, Moscow (1986).Google Scholar
  11. 11.
    G. V. Tkachenko and B. A. Uryukov, Heat transfer from a jet flowing into a closed cavity, J. Eng. Phys. Thermophys., 76, No. 1, 76–82 (2003).CrossRefGoogle Scholar
  12. 12.
    H. Miyazaki and E. Silberman, Flow and heat transfer on a flat plate normal to a two-dimensional laminar jet issuing from a nozzle of finite height, Int. J. Heat Mass Transf., 15, 2097−2107 (1972).CrossRefzbMATHGoogle Scholar
  13. 13.
    H. Schlichting, Theory of Boundary Layer [Russian translation], Nauka, Moscow (1977).Google Scholar
  14. 14.
    D. H. Lee, J. Song, and C. J. Myeong, The effect of nozzle diameter on impinging jet heat transfer and fluid flow, J. Heat Transf., 126, 554–557 (2004).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Material-Science ProblemsNational Academy of Sciences of UkraineKievUkraine

Personalised recommendations