IJPAM: Volume 19, No. 4 (2005)

SIMILARITY SOLUTIONS FOR BOUNDARY LAYER
FLOW ON A MOVING SURFACE IN AN OTHERWISE
QUIESCENT FLUID MEDIUM

Liancun Zheng$^1$, Xiaohong Su$^2$, Xinxin Zhang$^3$
$^{1,2}$Department of Mathematics and Mechanics
University of Science and Technology Beijing
Beijing, 100083, P.R. CHINA
e-mail: liancunzheng@sina.com
$^3$School of Mechanical Engineering
University of Science and Technology Beijing
Beijing, 100083, P.R. CHINA
e-mail: xxzhang@me.ustb.edu.cn


Abstract.This work considers the problem of boundary layer flow for a flat surface moving in an otherwise quiescent power law fluid medium. The laminar boundary layer equations are reduced to a singular nonlinear two-point boundary value problem by suitable similarity transformations. A rigorous proof of existence and uniqueness of solution to the boundary value problem is given and a theoretical estimation for skin friction coefficient is obtained. The reliability and efficiency of the proposed estimate formula are verified by numerical results with absolute errors obtained by lower bound no more than $ 0.0026 $ for power law exponent $n\geq 20$ and no more than $0.0004$ for power law exponent $n\geq 200$.

Received: March 18, 2005

AMS Subject Classification: 34B15, 76D10

Key Words and Phrases: power law fluids, nonlinear boundary value problems, positive solutions, existence and uniqueness, skin friction

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 4