Explicit equations for transient heat conduction in finite solids for <Emphasis Type="Italic">Bi</Emphasis> > 2

A set of correlations is developed for transient heat conduction in finite solids (plates, cylinders and spheres) exposed to high Biot number convection boundary conditions. For Bi ≥ 3, the error of the approximate solutions is well below 1% of the initial temperature difference driving the transient.     

Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model

In this paper, we proposed a model of generalized magneto-thermoelastic for orthotropic hollow cylinder whose surfaces are subjected to a thermal relaxation under the effect of rotation with one relaxation time. The system of fundamental equations is solved by using an implicit finite-difference scheme. A numerical method is used to calculate the temperature, displacement and the components of stresses with time and through the radial of the cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation, inhomogeneity and magnetic field are very pronounced. Comparison made with the results predicted by the theory of generalized magneto-thermoelasticity with one relaxation time in the absence of rotation.     

Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid

The unsteady laminar flow of an incompressible micropolar fluid over a stretching sheet is investigated. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. Effects of the unsteadiness parameter, material parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined.     

Patterns and heat transfer in Rayleigh-Bénard thermal gravitational convection in helium (<Superscript>3</Superscript>He) near the critical point

Thermal gravitational convection in a bottom-heated layer of near-critical ³He is considered. The range of criteria determining the convection parameters beyond the stability threshold is discussed. The specific features of 2D and 3D supercritical structures, the adiabatic compression effect, and heat transfer are considered.     

The Neumann boundary problem for axisymmetric fractional heat conduction equation in a solid with?cylindrical hole and associated thermal stress

The theory of thermoelasticity based on the heat conduction equation with the Caputo time-fractional derivative of order α is used to study thermal stress in an infinite medium with a cylindrical hole. Two types of Neumann boundary conditions are considered: the constant value of the normal derivative of the temperature and constant heat flux at the surface of a cavity. The solution is obtained applying Laplace and Weber integral transforms. Numerical results are illustrated graphically.     

A C<Superscript>0</Superscript>-type zig–zag theory and finite element for laminated composite and sandwich plates with general configurations

In order to conveniently develop C⁰ continuous element for the accurate analysis of laminated composite and sandwich plates with general configurations, this paper develops a C⁰-type zig–zag theory in which the interlaminar continuity of transverse shear stresses is a priori satisfied and the number of unknowns is independent of the number of layers. The present theory is applicable not only to the cross-ply but also to the angle-ply laminated composite and sandwich plates. On the premise of retaining the merit of previous zig–zag theories, the derivatives of transverse displacement have been taken out from the displacement fields. Therefore, based on the proposed zig–zag theory, it is very easy to construct the C⁰ continuous element. To assess the performance of the proposed model, the classical quadratic six-node triangular element with seven degrees of freedom at each node is presented for the static analysis of laminated composite and sandwich plates. The typical examples are taken into account to assess the performance of finite element based on the proposed zig–zag theory by comparing the present results with the three-dimensional elasticity solutions. Numerical results show that the present model can produce the more accurate deformations and stresses compared with the previous zig–zag theories.     

Entropy Solutions in <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">∞</Emphasis></Superscript> for the Euler Equations in Nonlinear Elastodynamics and Related Equations

A compactness framework is established for approximate solutions to the Euler equations in one-dimensional nonlinear elastodynamics by identifying new properties of the Lax entropies, especially the higher order terms in the Lax entropy expansions, and by developing ways to employ these new properties in the method of compensated compactness. Then this framework is applied to establish the existence, compactness, and decay of entropy solutions in L for the Euler equations in nonlinear elastodynamics with a more general stress-strain relation than those for the previous existence results. This compactness framework is further applied to solving the Euler equations of conservation laws of mass, momentum, and energy for a class of thermoelastic media, and the equations of motion of viscoelastic media with memory.     

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.     

Stability and implementable ℋ<Subscript>∞</Subscript> filters for singular systems with nonlinear perturbations

In this paper, we investigate the problem of designing ℋ_∞ filter for a class of continuous-time uncertain singular systems with nonlinear perturbations, which can be realized in practice. The perturbation is a time-varying function of the system state and satisfies a Lipschitz constraint. The design objective is to guarantee that a prescribed upper bound on an ℋ_∞ performance of the robust filter is attained for all possible energy-bounded input disturbances and all admissible uncertainties and which can be implemented on-line to get a good replica of the state. We first establish sufficient condition for the existence and uniqueness of solution to the singular system connected with the normal filter. Using a linear matrix inequality (LMI) format, we then provide a sufficient condition for the asymptotic stability of the realizable ℋ_∞ filter. Then by means of a convex analysis procedure the filter gain matrices are derived and an important special case is readily deduced. Finally, a numerical example is presented to illustrate the theoretical developments.     

On the convergence of successive Galerkin approximation for nonlinear output feedback <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

Although the formulation of the nonlinear theory of H _∞ control has been well developed, solving the Hamilton–Jacobi–Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H _∞ control via output feedback are presented. An example is presented illustrating the application of the algorithm.     

Mathematic modeling and characteristic analysis for dynamic system with asymmetrical hysteresis in vibratory compaction

We investigate dynamic characteristics of vibratory compaction system with asymmetrical hysteresis. An asymmetrical model derived from Bouc-Wen differential equation is employed to describe hysteretic behavior of vibration engineering. A practical polynomial expression for hysteretic restoring force is deduced to be substituted into standard equation of the system, assuming that the non-linearity of the restoring force is weak. An asymptotic method, which combines Krylov-Bogolyubov-Mitropolsky (KBM) method with harmonic balance (HB) method, is applied to analyze steady-state responses of the asymmetrical hysteretic system subjected to harmonic excitation. Dynamic responses, such as the restoring force time histories and frequency responses of the system for the first order approximate, are obtained. Furthermore, numerical solution obtained using Runge-Kutta method as well as results of experiments (asphalt compaction on the Beijing-Fuzhou highway) are compared with the asymptotic solution. These results investigated that asymmetrical hysteretic model and the methods applied in this paper are quite appropriate for engineering applications.     

Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.     

An implicit algorithm for hypoelasto-plastic and hypoelasto-viscoplastic endochronic theory in finite strain isotropic–kinematic-hardening model

This paper is concerned with objective stress update algorithm for elasto-plastic and elasto-viscoplastic endochronic theory within the framework of additive plasticity. The elastic response is stated in terms of hypoelastic model and endochronic constitutive equations are stated in unrotated frame of reference. A trivially incrementally objective integration scheme for rate constitutive equations is established. Algorithmic modulus consistent with numerical integration algorithm of constitutive equations is extracted. The implementation is validated by means of a set of simple deformation paths (simple shear, extension and rotation), two benchmark test in nonlinear mechanics (the necking of a circular bar and expansion of a thick-walled cylinder), a test which demonstrates the capabilities of the proposed model in simulation of cyclic loading and ratcheting in finite strain case (cyclically loaded notched bar) and finally, the analysis of a tensile test, which presents a shear band with a finite thickness independent of the finite element mesh using endochronic viscoplastic constitutive model.     

等参管单元及其在热传导问题边界元法中的应用Isoparametric tube elements and their application in heat conduction BEM analysis

采用边界元法（BEM ）求解实际工程问题时,很大一部分误差来自于离散误差。为此,本文基于Lagrange插值原理,提出了一种三维等参管单元边界元算法,该单元能很好地模拟管状结构的几何外形并对物理量进行高阶插值,大大地消除了离散误差。另外,当在边界元法中使用等参管单元时,提出了一种在等参平面内消除积分奇异性的方法。算例表明,本文算法具有划分网格少,求解精度高的优点。     

The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid

The Stokes and Rayleigh Stokes problems for a flat plate in a viscoelastic fluid has recently been generalized to an edge and an exact analytical solution is obtained. In this paper, the edge problem has further been extended to the case of a rectangular pipe and exact solutions are obtained for Maxwell and second grade fluids. Also, the flow due to an oscillating edge problem is extended to generalized Maxwell fluid.     

Turbulent Flow Around Fluid–Porous Interfaces Computed with a Diffusion-Jump Model for <Emphasis Type="Italic">k</Emphasis> and <Emphasis Type="Italic">ε</Emphasis> Transport Equations

Flow over vegetation and bottom of rivers can be characterized by some sort of porous structure of irregular surface through which a fluid permeates. Also, in engineering systems, one can have components that make use of a working fluid flowing over irregular layers of porous material. This article presents numerical solutions for such hybrid medium, considering here a channel partially filled with a flat porous layer saturated by a fluid flowing in turbulent regime. One unique set of transport equations is applied to both the regions. A diffusion-jump model for both the turbulent kinetic energy and its dissipation rate, across the interface, is presented and discussed upon. The discretization steps taken for numerically accommodating such model in the system of algebraic equations are presented. Numerical results show the effects of Reynolds number, porosity, and permeability on mean and turbulence fields. Results indicate that when negative values for the stress jump coefficient are applied, the peak of the turbulent kinetic energy distribution occurs at the macroscopic interface.     

Young’s modulus defect for the solid solution of hydrogen in palladium (PdH<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)

We use the internal friction method in the free vibration mode to study the temperature dependence of the spectra of dissipative losses and shear modulus in the Pd polycrystalline system, the PdH _x penetration solid solution, and in the dehydrogenized Pd system. Studying the spectra and shear moduli, we discovered that the hydrogen desorption from the α- and β-phases of the PdH _x system occurs completely after the first cycle of heating of this system. The temperature dependences of the shear modulus of the original and dehydrogenized systems coincide. The existence of dissipative processes in the solid solution is related to the mobility of hydrogen atoms in the face-centered cubic lattice of the Pd structure and provokes the appearance of peaks of losses on the modulus defect spectrum in the temperature region. We consider the possibility of describing the modulus defect in the framework of phenomenological models of elasticity. Dissolution of hydrogen atoms in a metal structure results in changes in the physical-mechanical characteristics of the obtained solid solutions compared with the original dehydrogenized metals.     

A Phase-Partitioning Model for CO<Subscript>2</Subscript>–Brine Mixtures at Elevated Temperatures and Pressures: Application to CO<Subscript>2</Subscript>-Enhanced Geothermal Systems

Correlations are presented to compute the mutual solubilities of CO₂ and chloride brines at temperatures 12–300°C, pressures 1–600 bar (0.1–60 MPa), and salinities 0–6 m NaCl. The formulation is computationally efficient and primarily intended for numerical simulations of CO₂-water flow in carbon sequestration and geothermal studies. The phase-partitioning model relies on experimental data from literature for phase partitioning between CO₂ and NaCl brines, and extends the previously published correlations to higher temperatures. The model relies on activity coefficients for the H₂O-rich (aqueous) phase and fugacity coefficients for the CO₂-rich phase. Activity coefficients are treated using a Margules expression for CO₂ in pure water, and a Pitzer expression for salting-out effects. Fugacity coefficients are computed using a modified Redlich–Kwong equation of state and mixing rules that incorporate asymmetric binary interaction parameters. Parameters for the calculation of activity and fugacity coefficients were fitted to published solubility data over the P–T range of interest. In doing so, mutual solubilities and gas-phase volumetric data are typically reproduced within the scatter of the available data. An example of multiphase flow simulation implementing the mutual solubility model is presented for the case of a hypothetical, enhanced geothermal system where CO₂ is used as the heat extraction fluid. In this simulation, dry supercritical CO₂ at 20°C is injected into a 200°C hot-water reservoir. Results show that the injected CO₂ displaces the formation water relatively quickly, but that the produced CO₂ contains significant water for long periods of time. The amount of water in the CO₂ could have implications for reactivity with reservoir rocks and engineered materials.     

Measurement of Strain Localization Resulting from Monotonic and Cyclic Loading at 650 <Superscript>∘</Superscript>C in Nickel Base Superalloys

A methodology is presented for the use of the oxide scale that develops in polycrystalline Ni-base superalloys at service temperature, as a speckle pattern for μm-scale resolution strain measurements. Quantitative assessment of the heterogeneous strain field at the grain scale is performed by high-resolution SEM digital image correlation under monotonic and cyclic loading in polycrystalline Ni-base superalloys up to 650 ^°C. In the René 88DT superalloy, strain localization is observed near twin boundaries during low cycle fatigue (LCF) at intermediate temperatures, correlating with activation of {111} 〈110〉 and {111} 〈112〉 slip systems. A strong correlation between the microstructural configuration that promotes strain localization during monotonic loading and crack initiation at 650 ^°C in low cycle fatigue was observed.