Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0931.76017
Liao, Shijun
A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate. (English)
[J] J. Fluid Mech. 385, 101-128 (1999). ISSN 0022-1120; ISSN 1469-7645/e

Summary: We apply a new analytic technique, namely the homotopy analysis method, to give an explicit, analytic, uniformly valid solution of the equation governing the two-dimensional laminar viscous flow over a semi-infinite flat plate, $f'''(\eta)+ \alpha f(\eta)f''(\eta)+ \beta[1- f^{\prime 2}(\eta)] =0$, under the boundary conditions $f(0)= f'(0)= 0$, $f'(+\infty)= 1$. This analytic solution is uniformly valid in the whole region $0\le \eta<+\infty$. For Blasius' (1908) flow ($\alpha= 1/2$, $\beta= 0$), this solution converges to Howarth's (1938) numerical result and gives analytic value $f''(0)= 0.332057$. For the Falkner-Skan (1931) flow ($\alpha=1$), it gives the same family of solutions as Hartree's (1937) numerical results, and provides a related analytic formula for $f''(0)$ when $2\ge \beta\ge 0$. Additionally, this analytic solution allows to prove that for $-0.1988\le \beta<0$, the Hartree's (1937) family of solutions possesses the property that $f'\to 1$ exponentially as $\eta\to +\infty$.

MSC 2000:: *76D10 Boundary-layer theory (incompressible fluids)
76M45 Asymptotic methods, singular perturbations

Keywords: Hartree's family of solution; Blasius' flow; Falkner-Skan flow; homotopy analysis method

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]