Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls  

作　　者：张燕 林平 司新辉 

机构地区：[1]Department of Mathematics and Mechanics,University of Science andTechnology Beijing [2]Department of Mathematics,University of Dundee

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第2期203-220,共18页应用数学和力学（英文版）

基　　金：supported by the Beijing Higher Education Young Elite Teacher Project(No.YETP0387);the Fundamental Research Funds for the Central Universities(Nos.FRF-TP-12-108A and FRF-BR13-023);the National Natural Science Foundation of China(Nos.51174028 and 11302024)

摘　　要：The cases of large Reynolds number and small expansion ratio for the asym- metric laminar flow through a two-dimensional porous expanding channel are considered. The Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation by introducing a time and space similar transformation. A singular perturbation method is used for the large suction Reynolds case to obtain an asymptotic solution by matching outer and inner solutions. For the case of small expansion ratios, we are able to obtain asymptotic solutions by double parameter expansion in either a small Reynolds number or a small asymmetric parameter. The asymptotic solutions indicate that the Reynolds number and expansion ratio play an important role in the flow behavior. Nu- merical methods are also designed to confirm the correctness of the present asymptotic solutions.The cases of large Reynolds number and small expansion ratio for the asym- metric laminar flow through a two-dimensional porous expanding channel are considered. The Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation by introducing a time and space similar transformation. A singular perturbation method is used for the large suction Reynolds case to obtain an asymptotic solution by matching outer and inner solutions. For the case of small expansion ratios, we are able to obtain asymptotic solutions by double parameter expansion in either a small Reynolds number or a small asymmetric parameter. The asymptotic solutions indicate that the Reynolds number and expansion ratio play an important role in the flow behavior. Nu- merical methods are also designed to confirm the correctness of the present asymptotic solutions.

关 键 词：singular perturbation method regular perturbation method porousexpanding channel expansion ratio 

分 类 号：O357.3[理学—流体力学]