This letter is concerned with the plane and axisymmetric stagnation-point flows and heat transfer of an electrically-conducting fluid past a stretching sheet in the presence of the thermal radiation and heat generation or absorption.The analytical solutions for the velocity distribution and dimensionless temperature profiles are obtained for the various values of the ratio of free stream velocity and stretching velocity,heat source parameter,Prandtl number,thermal radiation parameter,the suction and injection velocity parameter and magnetic parameter and dimensionality index in the series form with the help of homotopy analysis method(HAM).Convergence of the series is explicitly discussed.In addition,shear stress and heat flux at the surface are calculated.
Jing Zhu.Lian-Cun Zheng.Xin-Xin Zhang Department of Mathematics and Mechanics,University of Science and Technology Beijing,100083 Beijing,China Thermal Engineering Department,University of Science and Technology Beijing,100083 Beijing,China
The development of closed-loop control systems is one of the most effective ways to improve the stability of the keyhole status during keyhole plasma arc welding (K-PAW). Due to the disadvantages of the "one-pulse-one-keyhole" technology based on the conventional square current waveform, the controlled pulse welding current waveform is newly applied to control the keyhole open and close periodically. In order to realize the real-time control on the keyhole behavior with this advanced current waveform, welding experiments and system identification are conducted based on the classical control theory. One complete welding cycle can be divided into 3 periods. The keyhole establishing time is the most important time variable, which determines the keyhole behavior and welding process stability. At the same time, the averaged efflux plasma arc voltage during one pulse cycle can reflect the real keyhole dimension and status in a real-time manner. Therefore, two single-input-single-output (SISO) systems are proposed, in which keyhole establishing time and keyhole average dimension are taken as the system controlled variables respectively. Welding experiments are designed with the peak current varying randomly. Experiments show that the keyhole establishing time changes in an opposite direction to the varied peak current, and the averaged efflux plasma arc voltage varies with the same trend as the peak current. Based on the least squares technique and F test of classical system identification, second order difference equation for keyhole establishing time/peak current system and first order difference equation for keyhole average dimension/peak current system are obtained. It is proved that the calculated data by the two mathematical expressions are well matched with the measured data. The proposed research provides mathematical expressions and theoretical analysis to develop closed-loop systems for the controlled pulse K-PAW.
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.
