2010 Vol. 31, No. 7

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Effect of Non-Uniform Temperature Gradient and Magnetic Field on Onset of Marangoni Convection Heated From Below by a Constant Heat Flux
S. P. M. Isa, N. M. Arifin, R. Nazar, M. N. Saad
2010, 31(7): 765-771. doi: 10.3879/j.issn.1000-0887.2010.07.001
Abstract(1598) PDF(812)
Abstract:
The effect of magnetic field and a non-uniform temperature gradient on the Marangoni convection in a horizontal fluid layer, heated from below and cooled from above with a constantheat flux was investigated. A linear stability analysis was performed to undertake a detailed investigation. The influence of various parameters on the onset of convection was analyzed. Six non-uniform basic temperature profiles were considered and some general conclusions about their destabilizing effects were presented.
A Minimax Principle on Energy Dissipation of Incompressible Shear Flow
CHEN Bo, LI Xiao-wei, LIU Gao-lian
2010, 31(7): 772-780. doi: 10.3879/j.issn.1000-0887.2010.07.002
Abstract(1769) PDF(806)
Abstract:
Energy dissipation rate is one of the most important concepts in turbulence theory. Doering-Constantin's variational principle characterizes the upper bounds(maximum) of the tmie-averaged rate of viscous energy dissipation. In present study, an optmiization theoretic point of view was adopted to recast Doering-Constantin's formulation into a minimax principle for the energy dissipation of an incompressible shear flow. Then the Kakutaniminimax theorem in game theory was applied to obtain a set of conditions under which the maximization and the minimization in the minmiax principle are commutative. The results not only elucidate the spectral constraint of Doering-Constantin, but also confirm the equivalence of Doering-Constantin's variational principle and Howard-Busse's statistical turbulence theory.
General Solution for a Class of Time Fractional Partial Differential Equation
HUANG Feng-hui, GUO Bo-ling
2010, 31(7): 781-790. doi: 10.3879/j.issn.1000-0887.2010.07.003
Abstract(2389) PDF(1106)
Abstract:
A class of tmie fractional partial differential equation, including time fractional diffusion equation, tmie fractional reaction-diffusion equation, time fractional advection-diffusione-quation and their corresponding in teger-order partial differential equations, was considered. The fundam ental solutions for the Cauchy problem in a whole-space domain and signaling problem in a hal-fspace domain were obtained by using Fourier-Laplace trans forms and their inverse transforms. The appropriate structures for the Green functions were provided. On the other hand, the solutions in the form of a series for the in itial and boundary value p rob lem s in a bounded-space domain were derived by the Sine-Laplace or Cosine-Laplace transforms. Two examples were presented to show the application of the present technique.
Simple Waves for Two-Dimensional Pseudo-Steady Compressible Euler System
LAI Geng, SHENG Wan-cheng
2010, 31(7): 791-800. doi: 10.3879/j.issn.1000-0887.2010.07.004
Abstract(1832) PDF(878)
Abstract:
A simple wave was defined as a flow in a region whose image is a curve in phase space. It is well known that "the theory of smiple waves is fundamental in building up the solutions of flow problems out of elementary flow patterns". Geometric construction of simple waves for the 2D pseudo-steady compressible Euler system were mainly concerned with. Based on the geometric in terpretation the expansion or compress ion smiple wave flow construction around a pseudo-stream line with a bend part was constructed. It is a building block which appears in the global solution to four contact discontinuities Riemann problems.
Physical Criterion Study on Forward Stagnation Point Heat Flux CFD Computations at Hypersonic Speeds
LI Bang-ming, BAO Lin, TONG Bing-gang
2010, 31(7): 801-811. doi: 10.3879/j.issn.1000-0887.2010.07.005
Abstract(1529) PDF(827)
Abstract:
In order to evaluate the uncertainties in CFD computations of the stagnation point heat flux, a physical criterion was developed. Based on a quasi-one-dmiensional hypothesis along stagnation line, a new stagnation flow model was applied which contributes to obtain the governing equations of the flow near the stagnation point at hypersonic speeds. From the above equations, a set of compatibility relations was given at the stagnation point and along the stagnation line, which consist of the physical criterion for checking the accuracy in stagnation point heat flux computations. Eventually, verification of the criterion was made among various numerical results.
New Expression for Collision Efficiency of Spherical Nanoparticles in Brownian Coagulation
CHEN Zhong-li, YOU Zhen-jiang
2010, 31(7): 812-821. doi: 10.3879/j.issn.1000-0887.2010.07.006
Abstract(1428) PDF(863)
Abstract:
The collision efficiency of dioctyl phthalate nanoparticles in the Brownian coagulation was studied. A set of collision equations were solved numerically to find the relationship between the collision efficiency and the particle radius varying from 50 nm to 500 nm in the presence of Stokes resistance, lubrication force, vander Waals force and elastic deformation force. The calculated results are in agreement with the expermiental ones qualitatively. The results show that the collision efficiency decreases with the increase of particle radius in the range of 50 nm to 500 nm. Based on the numerical data a new express ion for collision efficiency was presented.
Streamline Diffusion Nonconforming Finite Element Method for the Time-Dependent Linearized Navier-Stokes Equations
CHEN Yu-mei, XIE Xiao-ping
2010, 31(7): 822-834. doi: 10.3879/j.issn.1000-0887.2010.07.007
Abstract(1825) PDF(852)
Abstract:
A finite difference streamline diffusion non conforming finite element approxmiation was proposed for solving the time-dependent linearized Navier-Stokes equations. Stream line diffusion finite element method was used to discretize the space variables in order to cope with the usual instabilities caused by the convection term and finite difference discretization was used in the time domain. Noncon forming finite element approxmiations were used for the velocity and pressure fields: the velocity is approxmiated by discontinuous piecewise linear and the pressure by piecewise constant. Stability and optimal error estimates for the discrete solutions are obtained.
Phragmén-Lindel-f and Continuous Dependence Type Results in a Stokes Flow
J. C. Song
2010, 31(7): 835-842. doi: 10.3879/j.issn.1000-0887.2010.07.008
Abstract(1528) PDF(734)
Abstract:
The asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder was investigated. With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder, it is shown that solutions either grow exponentially or decay exponentially in the distance from the finite end of the cylinder. In the latter case the effect of perturbing the equation parameters is also investigated.
Analytical Method on Bending of Composite Laminated Beams With Delaminations
HAN Hai-tao, ZHANG Zheng, LU Zi-xing
2010, 31(7): 843-852. doi: 10.3879/j.issn.1000-0887.2010.07.009
Abstract(1623) PDF(859)
Abstract:
Based on the first-order shear deformable beam theory, a refined model for composite beams containing a through-the-width delamination was presented, and the deformation at the delamination front was considered. Different from the ordinary delaminated beam theory, each of the perfectly bonded portions of the new model was constructed as two separated beams along the in terface, and the plane section assumption at the delamination front was released. The governing equations of the delaminated portions and bonded ones were established, combined with continuity conditions of displacements and internal forces. The solutions of delaminated composite beams with different boundary conditions, delamination locations and sizes were shown in excellent agreement with the finite element results, which demonstrate the efficiency and applicability of the presentmodel.
Elastic-Plastic Analysis of an Antiplane Crack Near the Crack Surface Region
YI Zhi-jian, GU Jian-yi, HE Xiao-bing, MA Ying-hua, YANG Qing-guo, PENG Kai, HUANG Feng, HUANG Zong-ming
2010, 31(7): 853-859. doi: 10.3879/j.issn.1000-0887.2010.07.010
Abstract(1614) PDF(820)
Abstract:
The elastic-plastic stress distribution and the elastic-plastic boundary configuration near the crack surface region are sign ificant but hard to obtain by means of conventional analysis. The crack line analysis method was developed through considering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length and the unit normal vector of the elastic-plastic boundary near the crack surface region were obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions have been abandoned during the analysis.
Some Qualitative Properties of Incompressible Hyperelastic Spherical Membranes Under Dynamic Loads
YUAN Xue-gang, ZHANG Hong-wu, REN Jiu-sheng, ZHU Zheng-you
2010, 31(7): 860-867. doi: 10.3879/j.issn.1000-0887.2010.07.011
Abstract(1444) PDF(795)
Abstract:
The nonlinear dynamic properties of axisymm etric deformation were examined for a sphericalm embrane composed of a transversely isotropic incompressible Rivlin-Saundersmaterial, where the membrane was subjected to periodic step loads at its inner and outer surfaces. A second order nonlinear ordinary differential equation that approxmiately describes the radially symmetric motion of the membrane was obtained by setting the thickness of the spherical structure close to 1 and the qualitative properties of the solutions were discussed in detail. In particular, the conditions that control the nonlinear periodic oscillation of the spherical membrane were proposed. Under certain cases, it was proved that the oscillating form of the spherical membrane would present a homoclinic orbit of type "∞" and that the growth of the amplitude of the periodic oscillation was discontinuous, and numerical results were also provided.
Group Classification for the Path Equation Describing Minimum Drag Word and Symmetry Reductions
Mehmet Pakdemirli, Yigit Aksoy
2010, 31(7): 868-873. doi: 10.3879/j.issn.1000-0887.2010.07.012
Abstract(1490) PDF(798)
Abstract:
Path equation describing minmium drag work first proposed by Pakdemirli [Pakdem irliM. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2009, 223(5): 1113-1116] was reconsidered. Lie Group theory was applied to the general equation. Group classification with respect to altitude dependent arbitrary function was presented. Using the symmetries, group-invariant solutions were determined and reduction of order by canonical coordinates was performed.
Quadratic Minimization for Equilibrium Problem Variational Inclusion and Fixed Point Problem
ZHANG Shi-sheng, LEE Joseph H W, CHAN Chi-kin
2010, 31(7): 874-883. doi: 10.3879/j.issn.1000-0887.2010.07.013
Abstract(1712) PDF(724)
Abstract:
The purpose was by using the resolvent approach to find the solutions to the quad-raticminimization problem: minx∈Ω||x||2, where Ω was the intersection set of the set of solutions to some generalized equilibrium problem, the set of common fixed points for an infinite family of nonexpansive mappings and the set of solutions to some variational in clusions in the setting of Hilbert spaces. Under suitable conditions some new strong convergence theorems for approximating to a solution of the above minimization problem were proved.
New Auxiliary Equation Method for Solving the KdV Equation
PANG Jing, BIAN Chun-quan, CHAO Lu
2010, 31(7): 884-890. doi: 10.3879/j.issn.1000-0887.2010.07.014
Abstract(1648) PDF(1047)
Abstract:
A new auxiliary equation method was used to find exact travelling wave solutions to the (1+1)-dmiensional KdV equation. Some exact travelling wave solutions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.