Green’s function solution for transient heat conduction in annular fin during solidification of phase change material

The Green’s function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.     

SOIL AGGREGATE AND ITS RESPONSE TO LAND MANAGEMENT PRACTICES

This paper provides a broad review of the existing study on soil aggregate and its responses to land management practices. Soil aggregate is used for structural unit, which is a group of primary soil particles that cohere to each other more strongly than other surrounding particles. The mechanism of soil particle aggregation may be expressed by a hierarchical model, which is based upon the hypothesis that macroaggregates （〉250μm） are collections of smaller microaggregates （〈250μm） held together with organic binding agents. Primary particles form microaggregates and then macroaggregates. Carbon （C）-rich young plant residues form and stabilize macroaggregates, whereas old organic C is occluded in the microaggregates. The interaction of aggregate dynamics with soil organic carbon （SOC） is complex and embraces a range of spatial and temporal processes within macroaggregates and microaggregates. The nature and properties of aggregates are determined by the quantity and quality of coarse residues and humic compounds and by the degree of their interaction with soil particles. The mechanisms resulting in the binding of primary soil particles into stable aggregates vary with soil parent material, climate, vegetation, and land management practices. Land management practices, including tillage methods, residue management, amendments, and soil fertility management, enhance soil aggregation. However, there is still much uncertainty in the dynamics of organic matter in macroaggregation and microaggregation, and research is still needed to understand further the mechanisms of aggregate formation and its responses to human activities.     

TRANSVERSE VIBRATION OF A HANGING NONUNIFORM NANOSCALE TUBE BASED ON NONLOCAL ELASTICITY THEORY WITH SURFACE EFFECTS

The aim of this paper is to study the free transverse vibration of a hanging nonuni- form nanoscale tube. The analysis procedure is based on nonlocal elasticity theory with surface effects. The nonlocal elasticity theory states that the stress at a point is a function of strains at all points in the continuum. This theory becomes significant for small-length scale objects such as micro- and nanostructures. The effects of nonlocality, surface energy and axial force on the natural frequencies of the nanotube are investigated. In this study, analytical solutions are formulated for a clamped-free Euler-Bernoulli beam to study the free vibration of nanoscale tubes.     

Some dynamical behavior of the Stuart-Landau equation with a periodic excitation

The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency are investigated in detail, respectively. The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al.     

Nonlinear three-dimension analysis for axially symmetrical circular plates and multilayered plates

Analytic nonlinear three-dimension solutions are presented for axially symmetrical homogeneous isotropic circular plates and multilayered plates with rigidly clamped boundary conditions and under transverse load.The geometric nonlinearily from a moderately large deflection is considered.A developmental perturbation method is used to solve the complicated nonlinear three-dimension differential equations of equilibrium.The basic idea of this perturbation method is using the two-dimension solutions as a basic form of the corresponding three-dimension solutions,and then processing the perturbation procedure to obtain the three-dimension perturbation solutions.The nonlinear three-dimension results in analytic expressions and in numerical forms for ordinary plates and multilayered plates are presented.All of the plate stresses are shown in figures.The results show that this perturbation method used to analyse nonlinear three-dimension problems of plates is effective.     

Two-dimensional complete rational analysis of functionally graded beams within symplectic framework

Exact solutions for generally supported functionally graded plane beams are given within the framework of symplectic elasticity. The Young’s modulus is assumed to exponentially vary along the longitudinal direction while the Poisson’s ratio remains constant. The state equation with a shift-Hamiltonian operator matrix has been established in the previous work, which is limited to the Saint-Venant solution. Here, a complete rational analysis of the displacement and stress distributions in the beam is presented by exploring the eigensolutions that are usually covered up by the Saint-Venant principle. These solutions play a significant role in the local behavior of materials that is usually ignored in the conventional elasticity methods but possibly crucial to the material/structure failures. The analysis makes full use of the symplectic orthogonality of the eigensolutions. Two illustrative examples are presented to compare the displacement and stress results with those for homogenous materials, demonstrating the effects of material inhomogeneity.     

Hall and ion slip effects on peristaltic flow and heat transfer analysis with Ohmic heating

The peristaltic transport of a magnetohydrodynamic （MHD） fluid is exam- ined for both symmetric and asymmetric channels. Hall and ion slip effects are taken into account. The heat transfer is analyzed by considering the effects of viscous and Ohmic dissipations. The relevant flow problems are first modeled, and then the closed form solutions are constructed under the assumptions of long wavelength and low Reynolds number. The solutions are analyzed through graphical illustration. It is noted that the velocity increases but the temperature decreases with the increases in the Hall and ion slip parameters. The axial pressure gradient is less in magnitude in the presence of Hall and ion slip currents. The Hall and ion slip effects are to decrease the maximum pres- sure against which peristalsis works as a pump. The free pumping flux decreases with the increases in the Hall and ion slip parameters. The increases in the Hall and ion slip parameters result in an increase in the size of the trapped bolus.     

UNSTEADY／STEADY NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY

A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.     

SOLUTION OF THE CONNECTION PROBLEMS BETWEEN A FINITE HOLED PLATE AND A STIFFENER BY USING THE PARTITIONING CONCEPT OF THE GENERALIZED VARIATIONAL METHOD

In this paper a new finite element method is presented.in which complex functions arechosen to be the finite element model and the partitioning concept of the generalizedvariational method is utilized.The stress concentration factors for a finite holed platewelded by a stiffener are calculated and the analytical solutions in series form are obtained.From some computer trials it is demonstrated that the problem of displacementcompatibility and continuity of tractions between the holed plate and the stiffener issuccessfully analysed by using this method.Since only three elements need to beformulated.relatively less storage is required than the usual finite element methods.Furthermore,the accurary of solutions is improved and the computer time requirements areconsiderably reduced.Numerical results of stress concentration factors and stresses alongthe welded-line which may be referential to engineers are shown in tables.     

Three-dimensional steady-state closed form solution for multilayered fluid-saturated anisotropic finite media due to surface/internal point source

A three-dimensional(3 D)steady-state solution of fluid saturated anisotropic finite media is presented.The eigenequation method and the pseudo-Stroh formalism are used to obtain the exact solution for homogeneous saturated finite media.The propagator matrix method is introduced to deal with the corresponding multilayered poroelastic media.The poroelastic solutions due to surface or internal point fluid source are obtained.The comparison of the results of the saturated isotropic media in a half space and those obtained by the finite element method is given to illustrate the accuracy of the solution in a finite domain.Numerical solutions of a sandwich poroelastic medium are presented to analyze its hydromechanical behaviors.Two ratios of the horizontal permeability to vertical permeability and different source positions are investigated.The results show that the fluid parameters and source positions have great influence on the hydromechanical behaviors of the layered media.     

Determination of elastic and plastic mechanical properties of dentin based on experimental and numerical studies

The aim of this study is to investigate the change of mechanical properties of human dentin due to aging and spatial variation. Sections of coronal dentin are made from human molars in three groups: young, mid-aged, and old patients. A nanoindentation test is conducted from regions near the pulp to the dentin-enamel junction (DEJ) to evaluate the load-depth indentation response and determine Young's modulus and hardness. Based on the loading and unloading load-displacement curves in nanoindentation, a numerical model of plastic damage is used to study the plastic and the damage behaviors and the contribution to the degradation in the unloading stiffness. The experimental results show that Young's modulus of the inner dentin is significantly lower than that of outer dentin in each age group. Compared with the young dentin, the old dentin has greater hardness and Young's modulus with similar spatial variations. The magnitudes of the yield strength and the damage variable are also affected by aging and vary with spatial locations. In the same age group, the yield strength in inner dentin is lower than those in middle and outer dentin, more damage occurs with similar spatial variations, and the yield strength of young dentin is generally lower and causes more damage compared with those in both the mid-aged and old groups.     

Free convection from one thermal and solute source in a confined porous medium

This paper reports a numerical study of double diffusive natural convection in a vertical porous enclosure with localized heating and salting from one side. The physical model for the momentum conservation equation makes use of the Darcy equation, and the set of coupled equations is solved using the finite-volume methodology together with the deferred central difference scheme. An extensive series of numerical simulations is conducted in the range of −10 ⩽ N ⩽ + 10, 0 ⩽ R _t ⩽ 200, 10⁻² ⩽ Le ⩽ 200, and 0.125 ⩽ L ⩽ 0.875, where N, R _t , Le, and L are the buoyancy ratio, Darcy-modified thermal Rayleigh number, Lewis number, and the segment location. Streamlines, heatlines, masslines, isotherms, and iso-concentrations are produced for several segment locations to illustrate the flow structure transition from solutal-dominated opposing to thermal dominated and solutal-dominated aiding flows, respectively. The segment location combining with thermal Rayleigh number and Lewis number is found to influence the buoyancy ratio at which flow transition and flow reversal occurs. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting segment.     

Viscoelastic properties of dibenzylidene sorbitol (DBS) physical gels at high frequencies

The rheological behavior of Dibenzylidene D-Sorbitol (DBS) gels formed in ethylene glycol, glycerol, mineral oil, ethanol, and chlorobenzene was studied using oscillatory squeezing flow viscometry. The storage (G ^′) and loss (G ^″) moduli were measured as a function of gellant concentration (0.5–2 w/w) and type of solvent. As expected greater values of gel strength (G ^′) were observed for gels containing higher concentrations of DBS. In addition, both storage and loss moduli of 2% systems were mostly frequency independent over the studied range, whereas 0.5% gels did exhibit some degree of dependence. We also found that the solvent plays an important role in the properties of the gels. Among the parameters that affect the viscoelastic properties of DBS gels, the solvent polarity and its ability to form hydrogen bonding may have significant effects on the gel rheology.     

Numerical calculations of supersonic underexpanded jets in a cocurrent flow with the use of parabolized Navier-Stokes equations

Results of a numerical study of three-dimensional supersonic jets propagating in a cocurrent flow are described. Averaged parabolized Navier-Stokes equations are solved numerically on the basis of a developed scheme, which allows calculations in supersonic and subsonic flow regions to be performed in a single manner. A jet flow with a cocurrent flow Mach number 0.05 ⩽ M_∞ ⩽ 7.00 is studied, and its effect on the structure of the mixing layer is demonstrated. The calculated results are compared with available experimental and numerical data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 54–63, May–June, 2008.     

Experimental determination of the friction factor coefficient in microchannels

Experimental data used to determine the friction factor in microchannels are presented. Glass microchannels with a circular cross section, diameters of 34.5, 33.6, and 24.5 μm, and different lengths are studied in the experiments. Pure deionized degassed water is used as a working fluid. The range of the Reynolds numbers is 13 ⩽ Re ⩽ 330. A method of two channels is used to calculate the friction factor. The results obtained are in good agreement with theoretical predictions for the case of a developed laminar flow in circular channels, but the use of the method of two channels has some constraints.     

Methods for Examining the Fatigue and Fracture Behavior of Hard Tissues

An understanding of the fatigue and fracture behavior of hard tissues (e.g., bone and tissues of the human tooth) is critical to the maintenance of physical and oral health. Recent studies suggest that there are a number of mechanisms contributing to crack extension and crack arrest in these materials, and that they appear to be a function of moisture and age of the tissue. An understanding of these processes can provide new ideas that are relevant to the design of multi-functional engineering materials. As a result, we have adopted the use of microscopic Digital Image Correlation (DIC) to examine the mechanisms of crack growth resistance and near-tip displacement distribution for cracks in human dentin that are subjected to opening mode loads. We have also developed a special compact tension (CT) specimen that permits evaluation of crack extension within small portions of tissue under both quasi-static and fatigue loads. The specimen embodies a selected portion of hard tissue within a resin composite restorative and enables an examination of diseased tissue, or portion with specific physiology, that would otherwise be impossible to evaluate. In this paper we describe application of these experimental methods and present some recent results concerning fatigue crack growth and stable crack extension in dentin and across the dentin-enamel-junction (DEJ) of human teeth.

A fractal model for thermal shrinkage of oriented polymers

A relationship between the amount of thermal shrinkage and the structural parameters of polyethylene extruded in the solid state and polymerization-filled compositions based on it is studied. It is shown that thermal shrinkage is determined by the fractal dimension of the polymer structure and the degree of stretching of the molecular chain. Galkin Donetsk Physicotechnical Institute, National Academy of Sciences of Ukraine, Donetsk 340114. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 160–163, January–February, 1998.     

Behaviour of the Reynolds stress on rough walls

Quadrant analysis is used to study the contributions, associated to the four quadrants of the (u,v) plane, to the production of the turbulent shear stress on rough walls. The measurements are described for a fully developed turbulent flow between two rough plates with varying the parameterλ _z(span/height ratio of roughness elements). The application of this technique indicates that the (Q ₂) events (ejections) and (Q ₄) events (sweeps) cause an intense production of the Reynolds stress —ρ as compared with the (Q ₁) and (Q ₃) quadrants. The (Q ₂) contribution to the Reynolds stress depends on the geometry factorλ _z. Variation of the parameterλ _zaffects the distributions of and forH⩽3, whereH is a particular threshold. Comparison with boundary layer flow shows that the region 0.2⩽y/h⩽0.7 is characterized by a Reynolds stress production, independent of the flow nature. The third moment of the longitudinal velocity fluctuations is found to be sensitive to the surface roughness.     

Effect of transverse shears on complex nonlinear vibrations of elastic beams

Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet’ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h²) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ⩽ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.     

Investigation of shrinkage-induced stresses in stereolithography photo-curable resins

An experimental study has been undertaken to investigate the shrinkage characteristics of acrylic-based and epoxy-based stereolithography (SL) photopolymer resin systems after they have been laser cured and post-cured under ultraviolet (UV), and thermal exposure. The induced residual stresses and strains were determined by the shadow moiré and the hole-drilling strain-gage methods. Out-of-plane displacements (warpage) of acrylic-based post-cured resin plates were recorded by means of the shadow moiré method and correlated to the shrinkage strains by theoretical analysis. The induced residual stresses in the epoxy-based cylindrical resin specimens were determined from strains of three-element strain-gage rosettes of the blind-hole drilling method. Results are presented for the shrinkage stresses and strains for both material systems as a function of the post-curing process (UV, thermal). It was found that the shrinkage strains in the acrylic-based photopolymer resin were of considerable magnitude, while thermal post-curing resulted in higher shrinkage stresses for both material systems. The values of the shrinkage stresses compare well with those of the existing literature.