The existence of similar solutions for some laminar boundary layer problems

1968 ◽  
Vol 31 (4) ◽  
pp. 288-303 ◽  
Author(s):  
J. B. McLeod ◽  
James Serrin
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Boundary Layer Problems ◽  
Similar Solutions

An Approximate Solution of the Laminar Boundary Layer on a Flat Plate with Uniform Suction

1955 ◽  
Vol 59 (538) ◽  
pp. 697-698
Author(s):  
S. J. Peerless ◽  
D. B. Spalding
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Present Method ◽  
Integral Method ◽  
Boundary Layer Thickness ◽  
Numerical Solutions ◽  
Approximate Methods ◽  
Boundary Layer Problems ◽  
Momentum Integral ◽  
Similar Solutions

Boundary layer problems may be divided into two classes: (a) those for which similar solutions can be found, i.e. where the boundary conditions are such that similar profiles differing only in scale factor exist at different sections; and (b) those where the boundary conditions do not effect similarity, so that the development of the boundary layer must be calculated in stages. The latter class are known as “continuation problems,” and very few numerical solutions have been obtained because of the labour involved.Approximate methods of solving continuation problems are known, using the Karman momentum integral method (e.g. Ref. 1) or variants. Some of these methods make use of velocity profiles calculated for “similar” boundary layers. This note presents a new approximate method which uses “similar” profiles but avoids using the momentum integral. Instead of characterising the boundary layer thickness by the “momentum thickness,” which needs to be calculated yet is of less direct interest, the wall shear stress is used; this stress usually has to be calculated in any case and the present method is therefore comparatively simple.

Similar and Asymptotic Solutions of the Incompressible Laminar Boundary Layer Equations with Suction

1967 ◽  
Vol 18 (2) ◽  
pp. 103-120 ◽  
Author(s):  
M. Zamir ◽  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Incompressible Flow ◽  
Suction Parameter ◽  
Suction Velocity ◽  
Boundary Layer Equations ◽  
Wide Range ◽  
Similar Solutions

SummarySimilar solutions of the boundary layer equations for incompressible flow with external velocity u1 ∞ xm and suction velocity υw ∞ x(m-1)/2 are obtained for negative values of m, in the range −0-1 to −0-9, and a wide range of suction quantities.The results are used, in combination with, existing solutions for positive m, to provide a guide to the ranges of m and suction parameter [(υw/u1√x] for which a general form of the classical asymptotic solution can be regarded as a good approximation to the exact solution.It is shown that the values of both m and suction parameter are generally important in this comparison, but for values of the latter greater than about 8 the approximation is a very good one for all values of m considered. For m≃−0·14 the approximation is good (i.e. the error is less than about 1 per cent) down to values of the suction parameter as low as 1·0.

The Calculation of Heat Transfer Coefficients from Skin Friction Coefficients in the Compressible Laminar Boundary Layer on an Aerofoil

1968 ◽  
Vol 19 (3) ◽  
pp. 243-253 ◽  
Author(s):  
R. E. Luxton
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Strong Dependence ◽  
Transfer Coefficients ◽  
Friction Coefficients ◽  
Heat Transfer Coefficients ◽  
Similar Solutions

SummaryIn this note a relation is established between the correlation parameters obtained by Cohen and Reshotko from similar solutions of the compressible laminar boundary layer, and the Pohlhausen-type pressure gradient parameter used in the approximate methods devised by Luxton and Young. A simple graphical procedure is presented to allow heat transfer coefficients to be obtained from known skin friction coefficients in the presence of a pressure gradient. In view of the restrictions of the similar solutions it cannot be claimeda priorithat the method gives accurate results. It does, however, reflect the strong dependence of the heat-transfer skin-friction relation on the pressure gradient and, by reference to calculated results published previously, it is suggested that the method may give adequate accuracy under quite severe conditions.

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