The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-...The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method （HAM） is used＇to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu＇s model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations axe transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α（t） from the initial state α0 to the final state al. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.展开更多
The flow of a viscoelastic fluid in porous channels with expanding or contracting walls is investigated.Using a similar transformation,the governing equations are reduced to a nonlinear fifth-order differential equati...The flow of a viscoelastic fluid in porous channels with expanding or contracting walls is investigated.Using a similar transformation,the governing equations are reduced to a nonlinear fifth-order differential equation.The homotopy analysis method is employed to obtain the expression for velocity fields.The analytical solutions are influenced by the permeation Reynolds number Re,the wall expansion ratio a and viscoelastic parameter w.Graphs are sketched and the effects of some values of parameters,especially the expansion ratio,on the velocity fields are discussed in detail.展开更多
The unsteady, laminar, incompressible, and two-dimensional flow of a mi- cropolar fluid between two orthogonally moving porous coaxial disks is considered. The extension of von Karman＇s similarity transformations is ...The unsteady, laminar, incompressible, and two-dimensional flow of a mi- cropolar fluid between two orthogonally moving porous coaxial disks is considered. The extension of von Karman＇s similarity transformations is used to reduce the governing partial differential equations （PDEs） to a set of non-linear coupled ordinary differential equations （ODEs） in the dimensionless form. The analytical solutions are obtained by employing the homotopy analysis method （HAM）. The effects of various physical param- eters such as the expansion ratio and the permeability Reynolds number on the velocity fields are discussed in detail.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 50936003 and50905013)the Open Project of State Key Laboratory for Advanced Materials (No. 2009z-02)
文摘The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method （HAM） is used＇to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu＇s model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations axe transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α（t） from the initial state α0 to the final state al. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.
基金Supported by the National Natural Science Foundations of China under Grant Nos 50936003 and 50905013the Open Project of State Key Laboratory for Advance Metals and Materials(2009Z-02)Research Foundation of Engineering Research Institute of USTB.
文摘The flow of a viscoelastic fluid in porous channels with expanding or contracting walls is investigated.Using a similar transformation,the governing equations are reduced to a nonlinear fifth-order differential equation.The homotopy analysis method is employed to obtain the expression for velocity fields.The analytical solutions are influenced by the permeation Reynolds number Re,the wall expansion ratio a and viscoelastic parameter w.Graphs are sketched and the effects of some values of parameters,especially the expansion ratio,on the velocity fields are discussed in detail.
基金Project supported by the National Natural Science Foundation of China (Nos. 51004013,50936003,51174028,and 50905013)the Research Foundation of Engineering Research Institute of University of Science and Technology Beijing (No. Yj2011-015)the Fundamental Research Funds for the Central Universities (No. T-RF-TP-12-108A)
文摘The unsteady, laminar, incompressible, and two-dimensional flow of a mi- cropolar fluid between two orthogonally moving porous coaxial disks is considered. The extension of von Karman＇s similarity transformations is used to reduce the governing partial differential equations （PDEs） to a set of non-linear coupled ordinary differential equations （ODEs） in the dimensionless form. The analytical solutions are obtained by employing the homotopy analysis method （HAM）. The effects of various physical param- eters such as the expansion ratio and the permeability Reynolds number on the velocity fields are discussed in detail.
