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Unformatted text preview: Correlation Methods for Integral Boundary Layers
We will look at one particularly well-known and easy method due to Thwaites in
First, start by slightly re-writing the integral b.l. equation. We had: τw
θ du e
+ (2 + H )
u e dx
ρ e u e dx
Multiply by u eθ : v τ wθ u eθ dθ θ 2 du e
(2 + H )
Then define λ = ue θ 2 du e d
dx du e v dx dx and this equation gives: ⎡τ θ
) = 2⎢ w − λ (2 + H )⎥
⎣ µu e
⎦ Thwaites then assumes a correlation exists which only depends on λ.
H = H (λ ) and τ wθ
= S (λ )
µu e shape factor
correlation shear correlation λ
dx du e ) ≅ 2[S (λ ) − λ (2 + H (λ )] ⇒ ue dx
now this is an approximation Correlation Methods for Integral Boundary Layers In a stroke of genius and/or luck, Thwaites looked at data from experiments and
known analytic solutions and found that
dx du e ≈ 0.45 − 6λ !!
dx This can actually be integrated to find: θ2 = 0.45v
ue 6 x ∫u 5
e dx o where we have assumed θ ( x = 0) = 0 for this. 16.100 2002 2 ...
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