Some perturbation solutions in laminar boundary layer theory Part 2. The energy equation

Fox, Herbert; Libby, Paul A.

doi:10.1017/s0022112064000830

Cited by 31 publications

(7 citation statements)

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“…They are of the form subject to boundary conditions G ( 0 ) = G(o0) = 0 (cf. Fox & Libby 1964). In the small-6, expansion, and in the large-el expansion, where, as before, 0 6 n < 1 and m is a non-negative integer.…”

Section: Appendix On the Existence Of Eigensolutions Steady Eigenfunmentioning

confidence: 91%

Two-dimensional boundary layers in a free stream which oscillates without reversing

Pedley

1972

J. Fluid Mech.

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The laminar boundary layer over the semi-infinite rigid plane y = 0, x > 0 is examined for the case when the free-stream velocity takes the form \[ U(x, t) = U_0(x) (1+\alpha_1 \sin \omega t), \] where 0 [les ] α1 < 1 and U0(x) ∝ xn, 0 [les ] n [les ] 1. The corresponding steady solution is the Falkner-Skan boundary layer with zero (n = 0) or favourable pressure gradient (n = 1 corresponds to the stagnation-point boundary layer). The skin friction, and the heat transfer from the wall when that is maintained at a uniform temperature T1 greater than the temperature T0 of the oncoming fluid, are calculated by means of two asymptotic expansions: a regular one for small values of the frequency parameter ε1(x) = ωx/U0(x) and a singular one (requiring the use of matched asymptotic expansions) for large values of ε1. The principal difference between this work and that of earlier authors is that here α1 is not required to be small. Numerical computations are made for three values of n (0, $\frac{1}{3}$, 1), three values of α1 (0·2, 0·5 and 0·8) and (in the case of the heat transfer) two values of the Prandtl number σ (0·72 and 7·1). It is demonstrated that for each n there is a value of ε1 at which the small-and the large-ε1 expansions for the skin friction overlap quite well, and that, near the overlap region, two terms of the small-ε1 expansion provide a more accurate asymptotic representation of the solution than three. It is also shown that there is no region of overlap between the small- and the large-ε1 heat-transfer expansions, except in one case (n = 1/3, σ = 0·72) where the overlap value of ε1 (= 2·0) is the same as for the skin-friction expansions. The question of the existence of eigensolutions in the large-ε1 expansion, where on physical grounds they can be expected to appear, is discussed in the appendix.

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Section: Appendix On the Existence Of Eigensolutions Steady Eigenfunmentioning

confidence: 91%

Two-dimensional boundary layers in a free stream which oscillates without reversing

Pedley

1972

J. Fluid Mech.

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“…and(4) are generalizations of those previously presented in Ref 1,. since for f j -^ oo there result the eigenfunctions for the case of constant wall enthalpy and for f i = 0 the eigenfunctions for the case of an adiabatic surface.As demonstrated in Ref.…”

mentioning

confidence: 65%

“…1 have been supplemented in the present work by the corresponding first ten values for f t = \ and the first nine values of f < = 4; these results are presented numerically in Table 1 and graphically in Fig. 1.…”

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confidence: 99%

Eigenvalues for the equation of species conservation with heterogeneous reaction

Janowitz

Libby

1964

AIAA Journal

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“…6 The functions U T (Y) and & T (Y) are obtained by dividing the 7 axis into segments and empirically fitting the data of Fig. 2 in each segment with a third-order polynomial, with continuity of the functions and first derivatives required at tie points.…”

Section: Initial Plane Of Datamentioning

confidence: 99%

Decay of streamwise vorticity downstream of a three-dimensional protuberance

et al. 1983

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Streamwise vortices generated in boundary layers are known to persist for hundreds of boundary-layer thicknesses. This remarkable property is the main topic of this paper. The particular case of the flowfield generated by a three-dimensional protuberance immersed in a flat plate boundary layer is studied using numerical modeling. Experimental measurements in a downstream crossflow plane are used to construct initial data for a marching calculation using the boundary-layer and boundary-region approximations; the latter includes crossflow diffusion terms. The former fails to predict the flowfield, but results from the latter agree qualitatively with aspects of the flowfield determined from the measurements of Tani et al. and are also in fair quantitative agreement.

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Some perturbation solutions in laminar boundary layer theory Part 2. The energy equation

Cited by 31 publications

References 3 publications

Two-dimensional boundary layers in a free stream which oscillates without reversing

Two-dimensional boundary layers in a free stream which oscillates without reversing

Eigenvalues for the equation of species conservation with heterogeneous reaction

Decay of streamwise vorticity downstream of a three-dimensional protuberance

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