Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-18T19:28:28.853Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)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), 1–23.Google Scholar
(2)Moore, F. K.Unsteady laminar boundary-layer flow. Nat. Adv. Comm. Aeronaut., Techn. Note 2471 (1951), 33 pages.Google Scholar
(3)Rosenhead, L. (editor). Laminar boundary layers (Clarendon, Oxford, 1963).Google Scholar
(4)Sarma, G. N.Solutions of unsteady boundary layer equations. Proc. Cambridge Philos. Soc. 60 (1964), 137–158.CrossRefGoogle Scholar
(5)Sarma, G. N.A general theory of unsteady compressible boundary layers with and without suction or injection. Proc. Cambridge Philos. Soc. 61 (1965), 795–807.Google Scholar
(6)Sarma, G. N.Unified theory for the solution of the unsteady thermal boundary-layer equation. Proc. Cambridge Philos. Soc. 61 (1965), 809–825.Google Scholar
(7)Sarma, G. N.Solutions of unsteady compressible boundary layer equations. Proc. Cambridge Philos. Soc. 62 (1966), 665.Google Scholar