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.
In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method （HAM） is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.
The traditional cyclical spectrum density（CSD） method is widely used to analyze the fault signals of rolling bearing. All modulation frequencies are demodulated in the cyclic frequency spectrum. Consequently, recognizing bearing fault type is difficult. Therefore, a new CSD method based on kurtosis（CSDK） is proposed. The kurtosis value of each cyclic frequency is used to measure the modulation capability of cyclic frequency. When the kurtosis value is large, the modulation capability is strong. Thus, the kurtosis value is regarded as the weight coefficient to accumulate all cyclic frequencies to extract fault features. Compared with the traditional method, CSDK can reduce the interference of harmonic frequency in fault frequency, which makes fault characteristics distinct from background noise. To validate the effectiveness of the method, experiments are performed on the simulation signal, the fault signal of the bearing outer race in the test bed, and the signal gathered from the bearing of the blast furnace belt cylinder. Experimental results show that the CSDK is better than the resonance demodulation method and the CSD in extracting fault features and recognizing degradation trends. The proposed method provides a new solution to fault diagnosis in bearings.
The flow of a micropolar fluid in a semi-porous channel with an expanding or contracting wall is investigated. The governing equations are reduced to ordinary ones by using similar transformations. To get the analytic solution to the problem, the homotopy analysis method （HAM） is employed to obtain the expressions for velocity fields. Graphs are sketched and discussed for various parameters, especially the effect of the expansion ratio on velocity and micro-rotation fields.
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.
