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A general theory of unsteady boundary-layer flows

Published online by Cambridge University Press:  24 October 2008

G. N. Sarma
G. N. Sarma
Affiliation:
University of Roorkee, India
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Abstract

The unsteady two-dimensional boundary-layer flows are investigated, using the equations linearized as by Lighthill. It is assumed, unlike separable forms and power functions taken by Sarma, that the perturbations which cause the unsteadiness in the flow are arbitrary functions of the distance along the flow and the time. In addition to the Reynolds number, it is explicitly assumed that the flow for large times is defined by a set of parameters like

ξ = φ/U0, U0(x) and φ (x are functions associated with the main stream in steady flow, λ(x, t) represents a perturbation, t time and x is the distance along the surface. This particular assumption is essentially an idea that is suggested by the work of Sarma. In solving the equations a number of free constants and arbitrary functions are used, which will be specified according to the given physical situation. For large times series solutions are assumed in terms of the above parameters and ultimately sets of differential equations are obtained in a single variable. Thus the theory makes the problem ready for computational work. For small times using the steady state solutions given in this paper, we proceed along the same lines as given in the work of Sarma. The velocity as well as thermal boundary layers are analysed in this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1309 - 1325
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

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