应用数学和力学

2012 Vol. 33, No. 3

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Conduction-Radiation Effect on Transient Natural Convection Along a Vertical Flat Surface With Thermophoresis

S.Mustafa Mahfooz, Md.Anwar Hossain

2012, 33(3): 265-279. doi: 10.3879/j.issn.1000-0887.2012.03.001

Abstract(1407) PDF(768)

Abstract:
The present paper concerns with the effect of thermophoretic particle deposition on the transient natural convection laminar flow along a vertical flat surface which was immersed in an optically dense gray fluid in the presence of thermal radiation. In the analysis the radiative heat flux term was expressed by adopting the Rosseland diffusion approximation. The governing equations were reduced to a set of parabolic partial differential equations which were then solved numerically with a finite difference scheme in the entire time regime,0 ≤τ < ∞.Asymptotic solutions were also obtained for sufficiently small and large times. Excellent agreement was found between the asymptotic and the numerical solutions. Moreover, the effects of different physical parameters, namely the thermal radiation parameter R_d,the surface temperature parameter θ_w, and the thermophoretic parameter λ,on the transient surface shear stress τ_w,the rate of surface heat transfer q_w, and the rate of species concentration m_w as well as on the transient velocity, temperature and concentration profiles were shown graphically for a fluid as air for which the Prandtl number Pr is 0.7 at 20℃ and 1 atm pressure.

Three Dimensional Channel Flow of Second Grade Fluid in a Rotating Frame

Saira Hussnain, Ahmer Mehmood, Asif Ali

2012, 33(3): 280-291. doi: 10.3879/j.issn.1000-0887.2012.03.002

Abstract(1349) PDF(916)

Abstract:
An analysis was performed for hydromagnetic second grade fluid flow between two horizontal plates in a rotating system in the presence of magnetic field. The lower sheet was considered to be a stretching sheet and the upper was a porous solid plate. By using suitable transformations the equations of conservation of mass and momentum were reduced to a system of coupled non-linear ordinary differential equations. Series solution of this coupled non-linear system was obtained by using the most powerful analytic technique Homotopy analysis method. The results were presented through graphs and the effects of non-dimensional parameters Re, λ, Ha², α and K² on the velocity field were discussed in details.

Unsteady Natural Convection Couette Flow of Heat Generating/Absorbing Fluid Between Vertical Parallel Plates Filled With Porous Material

Basant K.Jha, Muhammad K.Musa

2012, 33(3): 292-302. doi: 10.3879/j.issn.1000-0887.2012.03.003

Abstract(1205) PDF(714)

Abstract:
The extended Brinkman Darcy model for momentum equation, and an energy equation were 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 parallel plates) filled with fluidsaturated porous medium. The flow was triggered by the asymmetric heating and the acceleration motion of one of the bounding plates. The governing equations were simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain closed form solutions for the velocity and temperature profiles. Then the skin friction as well as the rate of heat transfer were consequently derived. It is noticed that at different sections within the vertical channel, the fluid flow as well as the temperature profile increase with time and 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 a Rheological Fluid: Model for Movement of Food Bolus Through Esophagus

J.C.Misra, S.Maiti

2012, 33(3): 303-319. doi: 10.3879/j.issn.1000-0887.2012.03.004

Abstract(1603) PDF(990)

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

Importance of Aging to the Dehydration Shrinkage of Human Dentin

WANG Rao-rao, MAO Shuang-shuang, Elaine Romberg, Dwayne Arola, ZHANG Dong-sheng

2012, 33(3): 320-331. doi: 10.3879/j.issn.1000-0887.2012.03.005

Abstract(1368) PDF(784)

Abstract:
There was an increase in the mineral content of human dentin with aging. Due to the consequent changes in mineral to collagen ratio, this process may influence the degree of hydrogen bonding that occurs with loss of water and the extent of shrinkage as a result of dehydration. Thus, the objective of this investigation was to quantify the differences in dehydration shrinkage of human dentin with patient age. Specimens of coronal dentin were 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 solution(HBSS). Dimensional changes of the dentin specimens occurring over periods of free convection were evaluated using microscopic digital image correlation(DIC). Results distinguished that the shrinkage of young dentin is significantly larger than that for old dentin, regardless of orientation and period of storage (p<0.01).Strains parallel to the tubules increased with proximity to the dentin enamel junction(DEJ) whereas the shrinkage strains in the transverse direction were largest in deep dentin (i.e. near the pulp). The degree of anisotropy in shrinkage increased from the pulp to the DEJ and was largest in young dentin.

Natural Frequency of Rotating Functionally Graded Cylindrical Shells

2012, 33(3): 332-341. doi: 10.3879/j.issn.1000-0887.2012.03.006

Abstract(1692) PDF(965)

Abstract:
Love’s first approximation theory was used to analyze the natural frequency of rotating functionally graded cylindrical shell. In order to verify the validity of the present method, natural frequencies of the simply supported nonrotating isotropic cylindrical shell and functionally graded cylindrical shell were compared with the available published results and good agreement was obtained. The effect of power law index, the wave number along the x and θdirection, thickness to radius ratio on natural frequencies of the simply supported rotating functionally graded cylindrical shell was investigated by several numerical examples. It is found that the fundamental frequencies of the backward waves increased with the increasing rotating speed while those of forward waves decreased with the increasing rotating speed, the forward and backward waves frequencies increased with the increasing thickness to radius ratio.

Fracture Analysis of a Mode-ⅡCrack Perpendicular to an Imperfect Bimaterial Interface

ZHONG Xian-ci, ZHANG Ke-shi

2012, 33(3): 342-352. doi: 10.3879/j.issn.1000-0887.2012.03.007

Abstract(1544) PDF(983)

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

On the Non-Existence of Shilnikov Chaos in Continuous-Time Systems

Zeraoulia Elhadj, J.C.Sprott

2012, 33(3): 353-356. doi: 10.3879/j.issn.1000-0887.2012.03.008

Abstract(1317) PDF(788)

Abstract:
A non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, smooth systems was obtained. Based on this result, and using an elementary example, it was conjectured that there was a fourth kind of chaos in polynomial ODE systems characterized by the nonexistence of homoclinic and heteroclinic orbits.

Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

SHEN Hai-long, SHAO Xin-hui, ZHANG Tie

2012, 33(3): 357-365. doi: 10.3879/j.issn.1000-0887.2012.03.009

Abstract(1239) PDF(842)

Abstract:
The preconditioned iterative methods for solving linear systems based on a class of weighted linear least square problems were proposed, which were the preconditioned generalized accelerated overrelaxation (GAOR) methods. Some convergence and comparison results were obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is indeed better than the rate of the original methods, whenever the original methods are convergent. Furthermore, effectiveness of the new preconditioned methods is shown by numerical experiment.

Completeness of the System of Root Vectors of Upper Triangular Infinite Dimensional Hamiltonian Operators Appearing in Elasticity Theory

WANG Hua, Alatancang, HUANG Jun-jie

2012, 33(3): 366-378. doi: 10.3879/j.issn.1000-0887.2012.03.010

Abstract(1312) PDF(917)

Abstract:
A class of upper triangular infinite dimensional Hamiltonian operators appearing in elasticity theory was dealt with. The geometric multiplicity and algebraic index of the eigenvalue were investigated, then further the algebraic multiplicity of the eigenvalue was obtained. Based on these properties,the concrete completeness formulation of the system of eigen or root vectors of the Hamiltonian operator was proposed. It is shown that this completeness is determined by the system of eigenvectors of its operator entries. Finally, some illustrating applications from elasticity theory are presented.