Transient electro-osmotic flow in cylindrical microcapillaries containing salt-free medium

A theoretical study on the transient electro-osmotic flow through a cylindrical microcapillary containing a salt-free medium is presented for both constant surface charge density and constant surface potential. The exact analytical solutions for the electric potential distribution and the transient electro-osmotic flow velocity are derived by solving the nonlinear Poisson-Boltzmann equation and the Navier-Stokes equation. Based on these results, a systematic parametric study on the characteristics of the transient electro-osmotic flow is detailed. The general behavior of transient electro-osmotic flow in a cylindrical tube is similar to that observed in a microchannel containing an electrolyte solution. However, the steady-state electro-osmotic flow significantly deviates from the typical plug flow at higher surface charge and the rate of increase in the electro-osmotic mobility is strongly suppressed due to the effect of counterion condensation. In addition, the applicability limit of these solutions is also discussed.     

Bounds of stability in heat conduction with internal heat generation

The criterion for the existence of a steady-state temperature distribution in a plane slab or system with internal heat generation is critically examined. The rate of heat generation from the non-uniformly populated heat sources in the slab is assumed to be linearly dependent on the temperature differential between the slab and the environment. The critical combination of the parameters under which the system can function satisfactorily is found to depend not only on the manner in which the heat sources are populated but also on the boundary conditions imposed on the system. The results of this study thus indicate that an inadvertent change from the designed boundary conditions can significantly alter the life span of the system.     

时动边界上热通量重构正问题求解方法

具有Neumann边界条件的抛物型方程的初边值问题是偏微分方程研究领域的一类经典的问题。正问题是由已知的边界条件和初始条件来求区域温度场的问题。若所给边界是固定区域的称为定边界问题,而现实中又有一类问题其边界随时间变化,这样的问题称为动边界问题。本文对于时动边界上的热通量重构正问题的求解提出了人工边界的方法。在人工边界的基础上采用了位势理论方法求解此定解问题,并与前面已经给出的差分方法进行了比较。为了检验方法的可行性和两种方法的优劣,给出了数值模拟。     

Optimal boundary control of heat conduction problems on an infinite time domain by control parameterization

The present paper deals with an optimal boundary control problem in which the process of systems under consideration is governed by a linear parabolic partial differential equation over an infinite time interval. The objective of the paper is to determine the optimal boundary control that minimize a given energy-based performance measure. The performance measure is specified as a quadratic functional of displacement and a suitable penalty term involving the boundary controls. In order to determine the optimal boundary controls, the problem with boundary controls are converted into a problem with distributed controls. The modal space technique is then used to reduce the system into the optimal control of time invariant lumped parameter system. The associated system of uncoupled first order initial value problems is solved in terms of controllers. Next step deals with the computation of the control and trajectory of the linear time-invariant lumped parameter. For this we approximate the controllers by a finite number of orthogonal exponential zero-interpolants over the interval [0,∞). The resultant performance index after using the optimality condition leads to a system of linear algebraic equations. The suggested technique is easy to implement on digital computer. We provide a numerical example to demonstrate the applicability and efficiency of the proposed approach.     

Simple inequalities in the vibrating string and heat conduction problems

Certain inequalities are presented, related to the L² norms of the solutions to the vibrating string and heat conduction partial differential equations; in particular, an “L² maximum principle” is derived for the heat equation, and similar inequalities for the vibrating string problem.     

A boundary residual method with heat polynomials for solving unsteady heat conduction problems

In this paper, we present a new method for solving unsteady heat conduction problems, which is based on a time–space boundary residual method with heat polynomials. More specifically, it employs an integral least squares criterion for the initial and boundary residuals so as to determine the unknown coefficients in a trial expansion of heat polynomials. Though it treats only one-dimensional cases, the present approach shows a good applicability for such heat conduction problems.     

一种新的径向导热界面参数插值格式

以变系数径向导热问题为研究对象,由傅里叶导热定律提出了较之文献更为合理的热导计算方法.根据流的相容性原理分别推导得出极坐标、柱坐标和球坐标系下新的界面半径和界面导热系数插值格式.通过几个变系数和非线性导热问题对插值格式进行考核,并与文献中的插值格式进行对比.结果表明,推导的格式充分考虑了变截面和变物性的综合影响,对于非线性和变系数导热问题能得到更精确的结果.     

Transient dipole radiation in an absorbing uniaxial crystal

The electromagnetic radiation arising from a longitudinally and a transversely oriented magnetic dipole in a dissipative uniaxially anisotropic medium is determined by writing separate equations for the electromagnetic field intensities, and utilizing a spectral representation in the space-time Fourier domain. It is established that explicit, time- dependent, analytical solutions are possible in the case where the permitivity, permeability and conductivity tensors are simultaneously diagonalizable by means of a collineatory transformation, and the permittivity and conductivity tensors are directly proportional to each other.     

End effects on the flow of heat,mass or electrical energy through a cylindrical rod

End effects on the flow of heat, mass or electrical energy through a cylindrical rod were investigated analytically. Three of the eight analytical solutions were evaluated on a $\text{360}\text{91}$ computer and compared with the results of a numerical analysis package dubbed “Heating III” to show that both compared favorably.Platinum and Hastelloy X rods were subjected to an electrical current applied via two electrodes, one covering one end and the application of the other being thesubject of this investigation. End effects based on voltage deviations of one part in a thousand or more were found to extend for a length to diameter ratio ranging from 0·6 to 1·9 depending upon whether the small electrode position being investigated was at the center of the end or on the periphery of the end. Calculated results from Heating III showed excellent agreement with the experimental results.In addition to their reported applications, the analytical solutions represent a contribution to a neglected area of applied mathematical physics and as such should prove equally useful in other areas that are dynamically analogous. Also the discontinuous infinite integral technique of solution has proven to be a very powerful one.     

Effects of a magnetic field on the free convective flow through a porous medium bounded by an infinite vertical porous plate with constant heat flux

This paper investigates the effects of a magnetic field on the free convective flow of a viscous, incompressible, dissipative fluid through a porous medium, occupying a semi-infinite region of the space bounded by an infinite vertical and porous plate. The plate is subjected to a normal suction velocity and the heat flux at the plate is constant. The magnetic field is of uniform strength and is applied perpendicular to the plate. An analytical solution to the problem is obtained. The influence of the magnetic parameter (M) and permeability parameter (K) is discussed for the case of air (P = 0.71) when the plate is subjected to a constant suction velocity and is being cooled by free convection currents.     

Adaptive unit-vector control of an uncertain heat diffusion process

This paper deals with the distributed tracking control of a heat process having uncertain diffusivity and subject to a distributed disturbance whose L₂ norm is bounded by a constant which is not known a priori. Under certain regularity assumptions on the disturbance and on the chosen reference profile, a distributed unit-vector control, with an adaptive magnitude, is designed which provides the asymptotic tracking of the reference. The logic governing the gain adaptation is gradient-based and monodirectional, i.e. the gain cannot decrease over time. Lyapunov arguments are invoked to support the convergence properties of the proposed scheme, whose performance are also investigated by means of computer simulations.     

价格影响消费的传导机制研究

在我国目前物价低迷状态下,价格因素对消费的影响往往被忽视。针对这一问题,提出了价格仍是影响消费的重要因素的观点。并利用统计分析方法对影响消费的价格因素进行分析,得出了消费不足的另一个(不同于收入的)传导机制,即固定资产投资↑→企业贷款量↑→企业成本↑→物价↑→购买力↓→消费↓→经济增长迟滞。目的在于适当降低固定资产投资、降低物价、刺激消费,进而拉动经济增长。     

Attitude tracking control of a quadrotor UAV in the exponential coordinates

A new approach to control the attitude of a quadrotor UAV in terms of the exponential coordinates is developed in this paper. The exponential coordinate is a minimal representation of the rotation matrix, but it can avoid singularities. Since the quadrotor UAV can be considered as a rigid body aircraft, the analytic closed-form expressions of a rigid body's attitude kinematics are derived from differential of exponential on SO(3). Furthermore, based on the exponential expressions of attitude kinematics, the controller of a fully actuated rigid body is designed using trajectory linearization control method. The overall attitude controller contains two loops, which are designed according to the torque equation and the angular velocity equation respectively. In the numerical simulation, the proposed attitude controller is compared to a controller in the Euler angles, showing that singularities induced by Euler angles are avoided by using exponential coordinates. The robustness test of the attitude controller is also demonstrated in the simulation. The simulation results indicate that the proposed method can be applied to the attitude tracking control of an aerial robot especially when the robot needs to make aggressive maneuverings.     

企业博士后科研工作站——一种有效的科技成果产业化的中介组织

当今世界,科学技术对经济增长的作用越来越明显,而科技成果产业化能力是衡量一个国家科技实力和技术创新能力的重要尺度,也是决定国家经济增长的关键因素,与发达国家相比,我国科技成果产业化能力较弱,在发达国家中,中介组织在促进科技成果产业化中占有重要的地位,而我国中介组织的作用还很薄弱,本文通过对企业博士后工作站在实施博士后制度之外所具有的科技成果产业化中介组织功能的论述,指出企业博士后工作站是一种有效的科技成果产业化中介组织.     

Predicting flow induced vibration in u-bend regions of heat exchangers: an engineering solution

From the standpoint of flow induced vibrations, U-bends of tubular heat exchangers constitute structurally one of the most vulnerable regions. The U-bends possess relatively low out-of-plane frequency enabling them to extract energy from the shell stream at low flow velocities. All published correlations in the literature imply the existence of a direct relationship between the flow velocities and the incidence of large ampitude tube vibrations. Hence it is important to determine the velocity profile in the U-bend region accurately. A method to obtain an engineering solution is proposed herein which may be utilized in conjunction with the available correlations to reliably predict the possibility of vibration. Determination of the flow profile may be further utilized to improve the estimates of shellside heat transfer coefficients.     

Numerical modeling of MHD stability in a cylindrical configuration

A numerical modeling of natural convection under the influence of either axial (B_z) or radial (B_r) magnetic field in a cylindrical configuration filled with a low-Prandtl number electrically conducting fluid, is studied. The finite volume method is used to discretize the equations of continuity, Navier Stokes and energy. A computer program based on the SIMPLER algorithm is developed. The flow and temperature fields are presented by stream function and isotherms, respectively. Stability diagrams are established according to the numerical results of this investigation. These diagrams put in evidence the dependence of the critical Grashof number, Gr_cr with the increase of the Hartmann number, Ha. The strongest stabilization of the convective flows occurs when the magnetic field is applied in the radial direction. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a radial magnetic field.     

dc electrokinetic transport of cylindrical cells in straight microchannels

Electrokinetic transport of cylindrical cells under dc electric fields in a straight microfluidic channel is experimentally and numerically investigated with emphasis on the dielectrophoretic (DEP) effect on their orientation variations. A two-dimensional multiphysics model, composed of the Navier–Stokes equations for the fluid flow and the Laplace equation for the electric potential defined in an arbitrary Lagrangian–Eulerian framework, is employed to capture the transient electrokinetic motion of cylindrical cells. The numerical predictions of the particle transport are in quantitative agreement with the obtained experimental results, suggesting that the DEP effect should be taken into account to study the electrokinetic transport of cylindrical particles even in a straight microchannel with uniform cross-sectional area. A comprehensive parametric study indicates that cylindrical particles would experience an oscillatory motion under low electric fields. However, they are aligned with their longest axis parallel to the imposed electric field under high electric fields due to the induced DEP effect.