低碳石灰煅烧合金罐内物料传热的近似计算

假定长柱状颗粒堆积体系为连续介质所建立的传热微分方程结合第一类齐次边界条件,得到了基于第一类Bessel函数的温度分布无穷级数表达式T（t,t）,近似计算了合金罐内颗粒石灰石的传热时间及物料预热对传热时间的影响,计算结果与工业化实验结果较为接近.     

A semi‐discrete approach to modelling and control of the continuous casting process

Starting from a partial differential equation describing the heat transfer in the continuous casting of steel, the Kirchhoff transformation is used to obtain a more simplified governing heat equation. A boundary state and control transformation is then introduced to obtain a nonlinear heat equation with boundary control. The semi‐discrete approximation is applied in the investigation to obtain an ordinary differential equation model. The derived lumped parameter control model can be used to get an approximate solution for the system as well as for finite dimensional system control studies. Finally, local controllability is proved for the system using a linearization technique.     

Correction Factors in Series Solutions for One- and Two-Dimensional Boundary Value Problems

A Fourier cum polynomial series solution with correction factors is presented herein for differential equations with variable coefficients. The differential equations correspond to a wide range of boundary value problems. The correction factors included herein are: (1) modified Lanczos correction; (2) Bessel J; and (3) loading correction factor. These correction factors are introduced in terms of Fourier and polynomial series. The main purpose of using correction factors through a set of series is to improve convergence of the proposed solution, using the first two terms of the series. For the loading correction factor, a Fourier series expansion coupled with orthogonality conditions leads to evaluating undetermined Fourier coefficients of arbitrarily applied loads using concepts of summation equations. Representative boundary value problems are provided to demonstrate the efficiency and accuracy of the first two terms of the proposed solution with correction factors.     

Modeling the Cooling of Concrete by Piped Water

Piped water is used to remove hydration heat from concrete blocks during construction. In this paper we develop an approximate model for this process. The problem reduces to solving a one-dimensional heat equation in the concrete, coupled with a first order differential equation for the water temperature. Numerical results are presented and the effect of varying model parameters shown. An analytical solution is also provided for a steady-state constant heat generation model. This helps highlight the dependence on certain parameters and can therefore provide an aid in the design of cooling systems.     

Bond Slip Analysis of Fiber-Reinforced Polymer-Strengthened Beams

The second order differential equation of interface shear is formulated for fiber-reinforced polymer-strengthened beams using beam theory with a shear deformable adhesive layer. The solution of the boundary value problem is obtained in closed form and is used to derive deflection expressions for different loading conditions. The solution is also extended to analyze partially plated beams. The results converge to the extreme cases of very poorly and perfectly bonded plates and they help identify values of the adhesive shear modulus for effective stiffening. Furthermore, the solution of partially plated beams aids in defining anchorage lengths needed to develop the full or the highest possible composite action at midspan.     

Using Finite-Element Method to Simulate Wave Transformations in Surf Zone

In this study, a finite element method proposed by Hsu et al. in 2003 is extended to develop a numerical model for the simulation of wave transformation in the surf zone. The governing equation is the elliptic mild-slope equation including the energy dissipation of wave breaking. At the open boundaries with varying depth, the reflected waves caused by shoaling are adopted to the radiation boundary conditions. The rationality of the present numerical model is examined through the cases of offshore parallel breakwater problems. The results of calculation are in good agreement with experimental results.     

Thermal stress and strain effects on phase transition temperatures in differential thermal analysis testing

The effects of thermal stress and strain on the solid-phase transition temperature in differential thermal analysis (DTA) were investigated both theoretically and experimentally. The thermal stress is caused by the nonuniform distribution of temperature in the sample, and the strain is caused by the phase transformation. The experimental materials included high-purity Zr, commercially pure Ti, and high-purity Fe. It was found that the effect of thermal stress on the solid-phase transformation temperature was negligible due to the small size of the sample. An equation relating the phase transition temperature and the heating rate was developed which contains both strain energy and grain boundary energy considerations. Equilibrium phase transition temperatures calculated using this equation for Zr, Ti, and Fe are in good agreement with the phase diagrams and previous work.     

硼钢的淬透性和硼淬透性因子及硼平衡集聚的研究

研究了硼淬透性因子与硼的晶界平衡集聚规律、钢的成分、奥氏体化温度及晶粒尺寸的关系。建立了硼的晶界平衡集聚方程。导出了由钢的成分（碳和合金元素）定量计算硼淬透性因子的二元回归方程。考察了硼淬透性因子随奥氏体化温度变化的单峰曲线规律；研究结果表明，硼钢的淬透性与奥氏体化温度无关。本还对传统的计算淬透性用各种图表进行了回归分析，建立了硼淬透性因子等一系列淬透性计算的关系式。     

Relation of anharmonicity to allotropie transformations in metals

The process of allotropic transformations of metals is discussed in terms of anharmonic effects due to thermal expansion and Grüneisen parameter. Any perturbation of the crystal structure at the transformation temperature is considered to be associated with some degree of expansion or compression of the atomic bonds without breaking or forming any new bonds. A thermodynamic equation relating the entropy change with the change in volume during transformation is derived from the equation of state for solids. A subsequent analysis of the relevant data from the literature supports the derived equation by showing the product of heat capacity at constant volume of a metal at its allotropie transformation point and Grüneisen parameter at 298 K to be approximately constant.     

The Simplex Method to Describe Hydrometallurgical Processes

A method for transformation of the differential equation in process hydrometallurgy was developed. This method uses a special simplex-logarithmic transformation equation to convert the original differential into a form convenient for analysis and calculation. The transformation is also useful for hydrometallurgical calculations in special complex situations and can be used to determine optimal regime for the application to equipment. This method is also used to handle general and special criteria similarity.     

Stress-corrosion cracking of sensitized type 304 stainless steel in thiosulfate solutions

The stress corrosion cracking of a sensitized Type 304 stainless steel has been studied at room temperature using controlled potentials and two concentrations of sodium thiosulfate. In both constant extension rate and constant load tests, the crack velocities attain extremely high values, up to 8 μm s^-1. Scratching electrode experiments conducted at various pH values on simulated grain boundary material show that both the crack initiation frequency and crack velocity are closely related to the repassivation rate of the grain boundary material as expected on a dissolution-controlled mechanism; however, the maximum crack velocity at any potential is consistently about two orders of magnitude higher than that predicted from the electrochemical data. Frequent grain boundary separation ahead of the crack tip is thought to occur, but retarded repassivation of the grain boundary material is a necessary feature of the cracking. Effects of strain-generated martensite are discussed.     

Flexural-Torsional Buckling of Cantilever Strip Beam-Columns with Linearly Varying Depth

In this paper, one investigates the elastic flexural-torsional buckling of linearly tapered cantilever strip beam-columns acted by axial and transversal point loads applied at the tip. For prismatic and wedge-shaped members, the governing differential equation is integrated in closed form by means of confluent hypergeometric functions. For general tapered members (0<(hmax?hmin)/hmax<1), the solution to the boundary value problem is obtained in the form of a Frobenius’ series, which is shown to converge in the interior of the domain and at the boundary if and only if 0<(hmax?hmin)/hmax<1/2. Therefore, for 1/2?(hmax?hmin)/hmax<1 the Frobenius’ series solution cannot be used to establish the characteristic equation for the cantilever beam-columns; the problem is then solved numerically by means of a collocation procedure. Some of the analytical solutions (buckling loads) were compared with the results of shell finite-element analyses and an excellent agreement was found in all cases, thus validating the mathematical model and confirming the correctness of the analytical results. The paper closes with a discussion on the convexity of the stability domain (in the load parameter space) and the accuracy of approximations based on Dunkerley-type theorems.     

Investigations to determine the maximum permissible cooling velocity for ceramic components made of alumina

The presented paper discusses the problems of heat stress arising as a result of instationary temperature fields (thermally induced stresses) in ceramic components and includes the results of both theoretical and experimental investigations to determine the critical cooling velocity for cylindrical bodies made of alumina. The theoretical and experimental results are compared to show that calculating the stresses using the linearized elasticity theory is sufficiently accurate. The fracture condition is determined so that the fracture stress ascertained in a 4-point-bending experiment is defined as the maximum bearable tensile stress. The statistical theory according to Weibull is applied to transform this fracture stress onto the type of stress occurring during the cooling experiments. In addition to a short derivation of the equations for thermally induced stresses with temperature-dependent material values, this paper also describes the determination of the relevant material values and, in particular, that of the temperature dependencies necessary for the calculation. The experimentally determined results show, in addition to the influence of the thermal diffusivity of the material, a quadratical dependence of the critical cooling velocity on the size of the body, as is also to be expected from an analytical solution to the stress equation.     

Least-Squares Finite-Element Evaluation of Flow Nets

A novel least-squares implementation of the finite-element method is presented to evaluate stream functions in the solution of field problems. The method is programmatically similar to the solution of the Laplace equation, and is based on the development of a stream field that is orthogonal to an already calculated potential field. The main advantage of the method comes from the fact that it eliminates the need of identification of boundary conditions for the stream functions. Implementation of this method requires that the Laplace equation be solved first to calculate the nodal potentials. The Laplace equation, with an identity conductivity matrix is then solved again to calculate the nodal values of the stream functions. One arbitrary boundary condition is sufficient for the second solution. Examples of cofferdam and curtained dam flow with isotropic as well as orthotropic soil conductivity are presented to demonstrate the method.     

Transformation behaviour of the high temperature martensitic steels with 8 – 14% chromium

Comprehensive development work on martensitic steels belonging to the so-called 12% Cr steel group were performed at the Institute for Materials Research (IMF) of Forschungszentrum Karlsruhe on martensitic steels, the so-called 12% Cr steel group, in order to meet the various requirements in nuclear and conventional energy technology. The transformation characteristics of 29 different grades of steel and 38 heats have been determined and continuous cooling transformation (CCT) diagrams have been prepared. The diagrams are first described by groups of subjects in a chronological order because the change in the chemical composition cannot be correlated in all cases with the change in transformation behaviour. The quenching hardness can be satisfactorily described as a function of the C+N content if, taking into account the Nb, Zr, Ta, Hf fractions, a common effectiveness factor is calculated. This effectiveness factor is also integrated in the calculation of the M_s point by modifying accordingly the equation proposed by Steven and Haynes for low-alloy steels and supplemented by the summands for V and W. An equation is introduced for the calculation of the critical cooling rate for pearlite transformation which takes into account the special influence exerted by elements Cr, V, Mo, W, Ge. The comparison between calculated and measured values for Ms and Vcrit is satisfactory, except for some steels.     

Green's Function for an Infinite Elastic Plateon Winkler's Foundation

In this technical note, an infinite thick plate on Winkler's foundation is studied. The effect of shear between the plate and the foundation on the deflection and the stresses is analyzed. It is assumed that the foundation has a stiffness k (the force needed to produce a unit displacement per area) and reacts in compression as well as tension. The effect of a concentrated normal unit force is investigated. The solution is based on the Airy stress function formulation. The Hankel transformation is employed to solve the biharmonic equation for the stress function. The transformed solution is subject to the transformed boundary conditions and the application of the inversion theorem leads to the final solution in the integral form. Judiciously selected dimensionless parameters make this solution relatively simple. Numerical results are obtained for some values of those parameters. In particular, the following two special cases are studied: (1) deflections of a relatively thin plate are compared to the results obtained by Timoshenko and Woinowsky-Krieger, giving an excellent correlation; and (2) with the thickness becoming infinite, the solution of Boussinesq's problem is readily recovered.     

Diffusion-controlled growth of disordered interphase boundaries in finite matrix

The diffusion-controlled growth of interphase boundaries in finite matrices, which is influenced by the enrichment or depletion of solute in the untransformed matrix, is investigated using the solution to the diffusion equation obtained from the general formulation of free boundary problems by Kolodner. The integro-differential equation for the boundary position and velocity derived from the flux balance of solute is numerically solved for both one-dimensional (planar growth) and three-dimensional cases (growth of a spherical interface toward its center) and compared with the quasi-stationary solution in corresponding situations. The results show that the latter solution coupled with the mass balance of solute between precipitate and matrix as previously utilized by some authors tends to overestimate the progress of transformation. The error becomes quite large at higher supersaturations where the quasi-stationary approximation obviously breaks down.     

Thermal Postbuckling of Laminated Composite Plates with Temperature Dependent Properties

The paper deals with the theoretical investigation of the postbuckling of laminated composite rectangular plates subjected to uniform in-plane temperature. An analytical method based on Chebyshev polynomial is employed. The formulation is based on Reissner–Mindlin plate theory and von Kármán nonlinear kinematics. The resulting nonlinear coupled differential equations are linearized using quadratic extrapolation technique. Double Chebyshev finite series is used to discretize the differential equations. An incremental iterative approach is employed for the solution. The effects of temperature dependent mechanical and thermal properties on the limiting/critical temperature and the postbuckling response are studied. The numerical results for different boundary conditions and lamination schemes are presented. Analysis results indicate that temperature dependent properties reduce the critical/limiting temperature and postbuckling strength.     

A novel numerical model for billet reheating furnace

A numerical model of billet reheating furnace is proposed, which includes heat fluxes calculation around four billet surfaces and two-dimensional conduction calculation inside billet. Radiation and convection heat fluxes on top and bottom surfaces are calculated simultaneously, based on quartic and linear difference between furnace gas and billet surface temperatures, while furnace gas temperature is determined according to thermocouple values along furnace length together with billet surface temperature. Lateral fluxes are also calculated considering angle factor on billets interval. Two-dimensional partial differential equation is acquired for billet conduction to determine temperature distribution, which is discretised and solved by Alternating Direction Implicit and TriDiagonal Matrix Algorithm. Two embedded thermocouple experiments were carried out to verify furnace gas temperature, the effect of billet interval on lateral heat flux calculation as well as billet temperature. It met agreement well with experiments on billet temperature, which could be a better prerequisite for further reheating furnace automatic control.     

Numerical Solution of 2D Free Surface Flow to Ditch Drains in Anisotropic Soils

A numerical solution of two-dimensional free surface flow to ditch drains in homogeneous and anisotropic soils is presented. The differential equation governing two dimensional ground-water flow in anisotropic soils is solved by the alternating direction implicit (ADI) method of finite difference. In the approach the method is modified to make it applicable for curved boundaries. This simplified approach does not involve any kind of smoothing or linearization technique. The model solutions for ditch drainage with constant replenishment and instantaneous drawdown are found to be in close agreement with the finite-difference and finite-element solutions proposed by other researchers.