Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1207.76050
Matthews, Miccal T.; Hill, James M.
Nano boundary layer equation with nonlinear Navier boundary condition. (English)
[J] J. Math. Anal. Appl. 333, No. 1, 381-400 (2007). ISSN 0022-247X

Summary: At the micro and nano scale the standard no slip boundary condition of classical fluid mechanics does not apply and must be replaced by a boundary condition that allows some degree of tangential slip. In this study the classical laminar boundary layer equations are studied using Lie symmetries with the no-slip boundary condition replaced by a nonlinear Navier boundary condition. This boundary condition contains an arbitrary index parameter, denoted by $n>0$, which appears in the coefficients of the ordinary differential equation to be solved. The case of a boundary layer formed in a convergent channel with a sink, which corresponds to $n=1/2$, is solved analytically. Another analytical but non-unique solution is found corresponding to the value $n=1/3$, while other values of $n$ for $n>1/2$ correspond to the boundary layer formed in the flow past a wedge and are solved numerically. It is found that for fixed slip length the velocity components are reduced in magnitude as n increases, while for fixed n the velocity components are increased in magnitude as the slip length is increased.

MSC 2000:: *76D05 Navier-Stokes equations (fluid dynamics)
35A30 Geometric theory for PDE, transformations
35Q35 Other equations arising in fluid mechanics
76A02 Foundations of fluid mechanics
76M60 Symmetry analysis, Lie group and algebra methods

Keywords: boundary layer; nonlinear Navier boundary condition; similarity solutions; nanofluidics

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