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.
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References
Yang, K. T.: Unsteady laminar boundary layers in an incompressible stagnation flow. J. Appl. Mech.25, 425–427 (1958).
Ma, P. K. H., Hui, W. H.: Similarity solutions of the two-dimensional unsteady boundary layer equations. J. Fluid Mech.216, 539–559 (1990).
Libby, P. A., Liu, T. M.: Some similar laminar flows obtained by quasilinearization. AIAA J.6, 1541–1548 (1968).
Rogers, D. F.: Reverse flow solutions for compressible laminar boundary layer equations. Phys. Fluids12, 517–523 (1969).
Wortman, A., Mills, A. F.: Separating self-similar laminar boundary layers. AIAA J.9, 2449–2451 (1971).
Rogers, D. F.: Comment on “Separating self-similar laminar boundary layers”. AIAA J.10, 1391–92 (1972).
Schlichting, H.: Boundary layer theory, pp. 95–98. New York: Mc Graw-Hill 1979.
Williams, J. C., Wang, T. J.: Semi-similar solutions of the unsteady compressible laminar boundary layer equations. AIAA J.23, 228–233 (1985).
Inouye, K., Tate, A.: Finite difference version of quasi-linearization applied to boundary layer equations. AIAA J.22, 558–560 (1974).
Wortman, A., Ziegler, H., Soo-Hoo, G.: Convective heat transfer at general three dimensional stagnation point. Int. J. Heat Mass Transfer14, 149–152 (1972).
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.
Varga, R. S.: Matrix iterative analysis. Englewood Cliffs: Prentice Hall 1962.
Williams, J. C.: Incompressible boundary layer separation. Ann. Rev. Fluid Mech.9, 113–144 (1977).
Smith, F. T.: Steady and unsteady boundary layer separation. Ann. Rev. Fluid Mech.18, 197 (1986).
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Subhashini, S.V., Nath, G. Unsteady compressible flow in the stagnation region of two-dimensional and axi-symmetric bodies. Acta Mechanica 134, 135–145 (1999). https://doi.org/10.1007/BF01312652
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DOI: https://doi.org/10.1007/BF01312652