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Unsteady laminar compressible boundary-layer flow at a three-dimensional stagnation point

Published online by Cambridge University Press:  12 April 2006

M. Kumari
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore 560012
G. Nath
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore 560012

Abstract

Unsteady laminar compressible boundary-layer flow with variable properties at a three-dimensional stagnation point for both cold and hot walls has been studied for the case when the velocity of the incident stream varies arbitrarily with time. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for two particular unsteady free-stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. The results indicate that the variation of the density-viscosity product across the boundary layer, the wall temperature and the nature of stagnation point significantly affect the skin friction and heat transfer.

Type
Research Article
Copyright
© 1978 Cambridge University Press

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References

Gribben, R. J. 1961 The laminar boundary layer on a hot cylinder fixed in a fluctuating stream. Trans. A.S.M.E., J. Appl. Mech. 28, 339.Google Scholar
Gribben, R. J. 1971 The fluctuating flow of a gas near a stagnation point on a hot wall. Trans. A.S.M.E., J. Appl. Mech. 38, 820.Google Scholar
Gross, J. F. & Dewey, C. F. 1965 Similar solutions of the laminar boundary layer equations with variable fluid properties. In Fluid Dyn. Trans. (ed. W. Fiszdon), vol. 2, p. 529. Pergamon.
Illingworth, C. R. 1958 The effects of a sound wave on the compressible boundary layer on a flat plate. J. Fluid Mech. 3, 471.Google Scholar
King, W. S. 1966 Low frequency, large amplitude fluctuations of the laminar boundary layer. A.I.A.A. J. 4, 994.Google Scholar
Libby, P. A. 1967 Heat and mass transfer at a general three-dimensional stagnation point. A.I.A.A. J. 5, 507.Google Scholar
Lighthill, M. J. 1954 The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc. Roy. Soc. A 224, 1.Google Scholar
Marvin, J. G. & Sheaffer, Y. S. 1969 A method for solving nonsimilar laminar boundary layer equations including foreign gas injection. N.A.S.A. Tech. Note D5516.Google Scholar
Moore, F. K. 1951 Unsteady laminar boundary layer flow. N.A.C.A. Tech. Note no. 2471.Google Scholar
Moore, F. K. & Ostrach, S. 1956 Average properties of a compressible laminar boundary layer on a flat plate with unsteady flight velocity. N.A.C.A. Tech. Note no. 3886.Google Scholar
Nath, G. & Muthanna, M. 1977 Laminar hypersonic boundary-layer flow at a three-dimensional stagnation point with slip and mass transfer. Int. J. Heat Mass Transfer 20, 1977.Google Scholar
Riley, N. 1975 Unsteady laminar boundary layers. SIAM Rev. 17, 274.Google Scholar
Stuart, J. T. 1972 Unsteady boundary layers. In Recent Research on Unsteady Boundary Layers, vol. 1, p. 1. Laval University Press, Quebec.
Telionis, D. P. 1975 Calculations of time dependent boundary layers. In Unsteady Aerodynamics (ed. R. B. Kinney), vol. 1, p. 155. University of Arizona, Tucson.
Telionis, D. P. & Gupta, T. R. 1977 Compressible oscillating boundary layers. A.I.A.A. J. 15, 974.Google Scholar
Vimala, C. S. & Nath, G. 1975 Unsteady laminar boundary layers in a compressible stagnation flow. J. Fluid Mech. 70, 561.Google Scholar