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Solutions of unsteady boundary-layer equations

Published online by Cambridge University Press:  24 October 2008

G. N. Sarma
Affiliation:
Presidency College, Madras, India

Abstract

The unsteady two-dimensional boundary-layer equations, linearized as by Lighthill are studied. A unified method is developed, from which the results for the stagnation flow, the flow along a flat plate, the flow in a converging canal, etc., can be derived as special cases. Solutions are obtained in two systems, one when the main stream is in unsteady motion and the wall is at rest and the other when the main stream is in steady motion and the wall is in an arbitrary motion. The stagnation flow has been done by Glauert and generalized by Watson. The flow along a flat plate and the flow in a converging canal are considered in detail.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Carslaw, H. S. and Jaeger, J. C.Operational methods in applied mathematics (Oxford, 1948).Google Scholar
(2)Glauert, M. B.The laminar boundary layer on oscillating plates and cylinders. J. Fluid Mech. 1 (1956), 97110CrossRefGoogle Scholar
(3)Goldstein, S. (editor). Modern developments in fluid dynamics, Vol. 1 (Oxford, 1938).Google Scholar
(4)Hartree, D. R.On an equation occurring in Falkner and Skan's approximate treatment of the equation of the boundary layer. Proc. Cambridge Philos. Soc. 33 (1937), 223239CrossRefGoogle Scholar
(5)Lighthill, M. J.The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc. Roy. Soc. London, Ser. A. 224 (1954), 123Google Scholar
(6)Mclachlan, N-W. Ordinary non-linear differential equations in engineering and physical sciences (Oxford, 2nd ed., 1956).Google Scholar
(7)Moore, F.K.Unsteady laminar boundary-layer flow. Nat. Adv. Comm. Aeronaut., Tech. Note 2471 (1951), 33 pages.Google Scholar
(8)Schlichting, H. (editor). Boundary layer theory (Pergamon, 1955).Google Scholar
(9)Watson, J.The two-dimensional laminar flow near the stagnation point of a cylinder which has., an arbitrary transverse motion. Quart. J. Mech. Appl. Math. 12 (1959), 175190CrossRefGoogle Scholar