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2012年 第33卷 第3期    刊出日期：2012-03-02

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论文

Book Review “Fabrikant, V. I. Contact and Crack Problems in Linear Theory of Elasticity, Bentham Science Publishers, Sharjah, UAE (2010)”

H. XIAO

2012, 33(3):  0. 

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Conduction-radiation effect on transient natural convection with thermophoresis

S. M. MAHFOOZ M. A. HOSSAIN

2012, 33(3):  271-288.  doi:10.1007/s10483-012-1549-6

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This paper discusses the effect of thermophoretic particle deposition on the transient natural convection laminar flow along a vertical flat surface, which is immersed in an optically dense gray fluid in the presence of thermal radiation. In the analysis, the radiative heat flux term is expressed by adopting the Rosseland diffusion approximation. The governing equations are reduced to a set of parabolic partial differential equations. Then, these equations are solved numerically with a finite-difference scheme in the entire time regime. The asymptotic solutions are also obtained for sufficiently small and large time. The obtained asymptotic solutions are then compared with the numerical solutions, and they are found in excellent agreement. Moreover, the effects of different physical parameters, i.e., the thermal radiation parameter, the surface temperature parameter, and the thermophoretic parameter, on the transient surface shear stress, the rate of surface heat transfer, and the rate of species concentration, as well as the transient velocity, temperature, and concentration profiles are shown graphically for a fluid (i.e., air) with the Prandtl number of 0.7 at 20?C and 1.013 × 105 Pa.

Three-dimensional channel flow of second grade fluid in rotating frame

S. HUSSNAIN A. MEHMOOD A.ALI

2012, 33(3):  289-302.  doi:10.1007/s10483-012-1550-9

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An analysis is performed for the hydromagnetic second grade fluid flow between two horizontal plates in a rotating system in the presence of a magnetic field. The lower sheet is considered to be a stretching sheet, and the upper sheet is a porous solid plate. By suitable transformations, the equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations. A series of solutions to this coupled non-linear system are obtained by a powerful analytic technique, i.e., the homotopy analysis method (HAM). The results are presented with graphs. The effects of non-dimensional parameters R, λ,M2, α, and K2 on the velocity field are discussed in detail.

Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material

B. K. JHA M.K.MUSA

2012, 33(3):  303-314.  doi:10.1007/s10483-012-1551-8

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The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel (formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium. The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates. The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles. Then, the skin friction and the rate of heat transfer are consequently derived. It is noticed that, at different sections within the vertical channel, the fluid flow and the temperature profiles increase with time, which are both higher near the moving plate. In particular, increasing the gap between the plates increases the velocity and the temperature of the fluid, however, reduces the skin friction and the rate of heat transfer.

Peristaltic transport of rheological fluid: model for movement of food bolus through esophagus

J. C. MISRA S.MAITI

2012, 33(3):  315-332.  doi:10.1007/s10483-012-1552-7

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Fluid mechanical peristaltic transport through esophagus is studied in the paper. A mathematical model has been developed to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths. The Ostwald-de Waele power law of a viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid. The model is formulated and analyzed specifically to explore some important information concerning the movement of food bolus through esophagus. The analysis is carried out by using the lubrication theory. The study is particularly suitable for the cases where the Reynolds number is small. The esophagus is treated as a circular tube through which the transport of food bolus takes place by periodic contraction of the esophageal wall. Variation of different variables concerned with the transport phenomena such as pressure, flow velocities, particle trajectory, and reflux is investigated for a single wave as well as a train of periodic peristaltic waves. The locally variable pressure is seen to be highly sensitive to the flow index “n”. The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.

Importance of aging to dehydration shrinkage of human dentin

汪饶饶 毛霜霜 E.ROMBERG D. AROLA 张东升

2012, 33(3):  333-344.  doi:10.1007/s10483-012-1553-8

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There is an increase in the mineral content of human dentin with aging. Due to the consequent changes in the mineral to the collagen ratio, this process may influence the degree of hydrogen bonding that occurs with the loss of water and the extent of shrinkage as a result of dehydration. Thus, the objective of this investigation is to quantify the differences in the dehydration shrinkage of human dentin with patient age. Specimens of coronal dentin are prepared from the molars of young (23  age  34) and old (52  age  62) patients, and then maintained in storage solutions of water or hanks balanced salt solutions (HBSS). Dimensional changes of the dentin specimens occurring over periods of free convection are evaluated by using the microscopic digital image correlation (DIC). The results distinguish that the shrinkage of the young dentin is significantly larger than that of the old dentin, regardless of the orientation and period of the storage. The strains parallel to the tubules increase with proximity to the dentin enamel junction (DEJ), whereas the shrinkage strains in the transverse direction are the largest in the deep dentin (i.e., near the pulp). The degree of anisotropy in the shrinkage increases from the pulp to the DEJ, and is the largest in the young dentin.

Natural frequencies of rotating functionally graded cylindrical shells

项松 李广超 张魏 杨明绥

2012, 33(3):  345-356.  doi:10.1007/s10483-012-1554-6

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Love’s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells. To verify the validity of the present method, the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results. Good agreement is obtained. The effects of the power law index, the wave numbers along the x- and θ-directions, and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples. It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed, the fundamental frequencies of the forward waves decrease with the increasing rotating speed, and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.

Fracture analysis of mode-II crack perpendicular to imperfect bimaterial interface

钟献词 张克实

2012, 33(3):  357-370.  doi:10.1007/s10483-012-1555-9

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The problem of a mode-II crack close to and perpendicular to an imperfect interface of two bonded dissimilar materials is investigated. The imperfect interface is modelled by a linear spring with the vanishing thickness. The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel. The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation. Several special cases of the mode-II crack problem with an imperfect interface are studied in detail. The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically. The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.

Non-existence of Shilnikov chaos in continuous-time systems

Z. ELHADJ J.C.SPROTT

2012, 33(3):  371-374.  doi:10.1007/s10483-012-1556-7

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In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained. Based on this result and an elementary example, it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation (ODE) systems characterized by the nonexistence of homoclinic and heteroclinic orbits.

Preconditioned iterative methods for solving weighted linear least squares problems

沈海龙 邵新慧 张铁

2012, 33(3):  375-384.  doi:10.1007/s10483-012-1557-x

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A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation (GAOR) methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

王华 ALATANCANG 黄俊杰

2012, 33(3):  385-398.  doi:10.1007/s10483-012-1558-x

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This paper deals with a class of upper triangular infinite-dimensional Hamiltonian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.