Acta Mechanica

, Volume 134, Issue 3–4, pp 135–145 | Cite as

Unsteady compressible flow in the stagnation region of two-dimensional and axi-symmetric bodies

  • S. V. Subhashini
  • G. Nath
Original Papers
Received:

Summary

This paper deals with a new similarity solution of unsteady laminar compressible two-dimensional and axi-symmetric boundary layers. It has been shown that a self-similar solution is possible when the free stream velocity varies inversely with time. The two-point boundary value problems governed by self-similar equations have been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. It is observed that the effect of the acceleration parameter (A) in the free stream velocity on the skin friction is more pronounced compared to the heat transfer. For certain values of the acceleration parameter and the total enthalpy at the wall, the surface shear stress (skin friction) vanishes. The skin friction and heat transfer increase due to suction, and the effect of injection is found to be just opposite. Velocity profiles are presented with reverse flow and without reverse flow depending on the values of toal enthalpy at the wall and the acceleration parameter.

Keywords

Heat Transfer Skin Friction Reverse Flow Finite Difference Scheme Compressible Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Yang, K. T.: Unsteady laminar boundary layers in an incompressible stagnation flow. J. Appl. Mech.25, 425–427 (1958).Google Scholar
  2. [2]
    Ma, P. K. H., Hui, W. H.: Similarity solutions of the two-dimensional unsteady boundary layer equations. J. Fluid Mech.216, 539–559 (1990).Google Scholar
  3. [3]
    Libby, P. A., Liu, T. M.: Some similar laminar flows obtained by quasilinearization. AIAA J.6, 1541–1548 (1968).Google Scholar
  4. [4]
    Rogers, D. F.: Reverse flow solutions for compressible laminar boundary layer equations. Phys. Fluids12, 517–523 (1969).Google Scholar
  5. [5]
    Wortman, A., Mills, A. F.: Separating self-similar laminar boundary layers. AIAA J.9, 2449–2451 (1971).Google Scholar
  6. [6]
    Rogers, D. F.: Comment on “Separating self-similar laminar boundary layers”. AIAA J.10, 1391–92 (1972).Google Scholar
  7. [7]
    Schlichting, H.: Boundary layer theory, pp. 95–98. New York: Mc Graw-Hill 1979.Google Scholar
  8. [8]
    Williams, J. C., Wang, T. J.: Semi-similar solutions of the unsteady compressible laminar boundary layer equations. AIAA J.23, 228–233 (1985).Google Scholar
  9. [9]
    Inouye, K., Tate, A.: Finite difference version of quasi-linearization applied to boundary layer equations. AIAA J.22, 558–560 (1974).Google Scholar
  10. [10]
    Wortman, A., Ziegler, H., Soo-Hoo, G.: Convective heat transfer at general three dimensional stagnation point. Int. J. Heat Mass Transfer14, 149–152 (1972).Google Scholar
  11. [11]
    Gross, J. F., Dewey, C. F.: Similar solutions of the laminar boundary layer equations with variable gas properties. In: Fluid dynamics transactions (Fiszdon, W., ed.), pp. 529–548. New York: Pergamon Press 1965.Google Scholar
  12. [12]
    Varga, R. S.: Matrix iterative analysis. Englewood Cliffs: Prentice Hall 1962.Google Scholar
  13. [13]
    Williams, J. C.: Incompressible boundary layer separation. Ann. Rev. Fluid Mech.9, 113–144 (1977).Google Scholar
  14. [14]
    Smith, F. T.: Steady and unsteady boundary layer separation. Ann. Rev. Fluid Mech.18, 197 (1986).Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • S. V. Subhashini
    • 1
  • G. Nath
    • 2
  1. 1.Department of Applied MathematicsBirla Institute of TechnologyRanchiIndia
  2. 2.VaranasiIndia

Personalised recommendations