带球形空腔的广义热弹性无限大材料的弹性模量和传热系数与材料参考温度的相关性

利用具某一松弛时间的广义热弹性方程求解了带球形空腔的无限大材料问题．该材料的弹性模量和传热系数是可变的．空腔的内表面没有力作用,但有热冲击作用．利用Laplace变换求得直接逼近解．数值求解了Laplace逆变换．给出了温度、位移和应力的分布图．     

Effect of process parameters on injection compression molding of pickup lens

The residual stresses and shrinkages of pickup lens in injection compression molding are investigated in this study. It was realized that the behavior of residual stresses in injection compression molding parts was affected by different process conditions such as melt temperature, mold temperature, compression pressure and time. Moldings under different conditions were numerically investigated to study the effects of the process conditions on the residual stresses and shrinkage of a pickup lens with large thickness variations. The mold temperature and compression were found to be the most important factors that affect the shrinkage of lens in the thickness direction, resulting in surface profile deviation. The effect of heat transfer coefficient of the mold wall used in the molding simulation was also discussed.     

Melting heat and mass transfer in stagnation point micropolar fluid flow of temperature dependent fluid viscosity and thermal conductivity at constant vortex viscosity

Steady mixed convection micropolar fluid flow towards stagnation point formed on horizontal linearly stretchable melting surface is studied. The vortex viscosity of micropolar fluid along a melting surface is proposed as a constant function of temperature while dynamic viscosity and thermal conductivity are temperature dependent due to the influence of internal heat source on the fluid. Similarity transformations were used to convert the governing equation into non-linear ODE and solved numerically. A parametric study is conducted. An analysis of the results obtained shows that the flow-field is influenced appreciably by heat source, melting, velocity ratio, variable viscosity and thermal conductivity.     

Axisymmetric boundary layers on non-uniformly heated horizontal surfaces

Similarity solutions for the velocity and temperature induced by axisymmetrically heated horizontal surfaces with a power law temperature distribution are derived and investigated. Two physical situations, a stationary and a radially moving temperature distribution are considered; both above and below the surface. Apart from a perturbation solution for small temperature differences for the latter, the equations have to be numerically integrated. The results include the non-existence of a solution below the surface for particularly large heat inputs. A major difference from previous work on cartesian geometries is that there must be a non-zero heat flux between the surface and fluid, which is related to the total heat flux through the fluid.     

Dynamic model for a magnetorheological damper

A lumped mass thermo-mechanical model for the dynamics of a damper filled with a magnetorheological fluid is described, analyzed, and numerically simulated. The model includes friction and temperature effects, and consists of a differential inclusion for the piston displacements coupled with the energy balance equation for the temperature. The fluid viscosity is assumed to be a function the temperature and electrical current, which in practice may be used as the control variable. Numerical simulations of the system behavior are presented. In particular, the simulations of an initial impact show how the subsequent oscillations can be effectively damped.     

地温“流”泛导的溃变与地震预报

本文在泛系的广义转化、优化和泛导变变关系中的非线性动力系统的溃变理论［１，２］的启发下，利用［２］的方法显化了非线性热传导方程的溃变与实际的地温‘流’演变类似·为此，作者结合１９７６年唐山大地震进行了相应的模拟·结果表明：地震前后的地温‘流’溃变可以用于地震预报，对唐山大地震约有５个月的预见期·若地温‘流’体现地壳运动的不可积的泛导方程，在信息充分的条件下，显化其溃变机理，则地震（地壳断裂）是可预报的     

Thermal shock fracture of a crack in a functionally gradient half-space based on the memory-dependent heat conduction model

In the present study, we consider a thermoelastic half-space made of a functionally gradient material with an insulated crack, which is subjected to a thermal impact. The memory-dependent heat conduction model is adopted for analysis. By using the Fourier and Laplace transforms, the thermoelastic problem is formulated in terms of singular integral equations which can be solved numerically. Effects of the time delay, kernel function, and nonhomogeneity parameters on the temperature and stress intensity factor are analyzed. Our results are also compared with those based on the Fourier and CV heat conduction models, which can be viewed as two special cases of the present model. In conclusion, the memory-dependent derivative and nonhomogeneity parameters play an essential role in controlling the heat transfer process.     

Cooling of a cylindrical container blasted into the rock

An upright cylindrical container blasted into the rock is filled instantaneously with a warm liquid. Heat is transferred from the liquid into the surrounding rock and the open air. The temperature of the liquid and the surrounding rock is determined as a function of time.The differential equation and the auxiliary conditions of the transient heat conduction problem are Laplace transformed, the subsidiary equations are solved by two-dimensional relaxation, and the resulting temperature is obtained by means of numerical inversion of the Laplace transform.The results are presented numerically and graphically.     

Inverse heat conduction problem in a thin circular plate and its thermal deflection

An inverse problem of transient heat conduction in a thin finite circular plate with the given temperature distribution on the interior surface of a thin circular plate being a function of both time and position has been solved with the help of integral transform technique and also determine the thermal deflection on the outer curved surface of a thin circular plate defined as 0 ? r ? a, 0 ? z ? h. The results, obtained in the series form in terms of Bessel’s functions, are illustrated numerically.     

Natural convection boundary layer flow of fluid with temperature-dependent viscosity from a horizontal elliptical cylinder with constant surface heat flux

This study deals with the temperature-dependent viscosity effects on the natural convection boundary layer on a horizontal elliptical cylinder with constant surface heat flux. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the heat transfer characteristics are presented as functions of eccentric angle for various values of viscosity variation parameters, Prandtl numbers and aspect ratios. Results show that an increase in the viscosity variation parameter tends to accelerate the fluid flow near the surface and increase the maximum velocity, thus decreasing the velocity boundary layer thickness. As the viscosity variation parameter is increased, the surface temperature tends to decrease, thus increasing the local Nusselt number. Moreover, the local Nusselt number of the elliptical cylinder increases as the Prandtl number of the fluid is increased.     

Saint–Venant torsion of a circular bar with radial cracks incorporating surface elasticity

The Saint–Venant torsion problem of a circular cylinder containing a radial crack with surface elasticity is studied. The surface elasticity is incorporated into the crack faces by using the continuum-based surface/interface model of Gurtin and Murdoch. Both an internal crack and an edge crack are considered. By using the Green’s function method, the boundary value problem is reduced to a Cauchy singular integro-differential equation of the first order, which can be numerically solved by using the Gauss–Chebyshev integration formula, the Chebyshev polynomials and the collocation method. Due to the incorporation of surface elasticity, the stresses exhibit the logarithmic singularity at the crack tips. The torsion problem of a circular cylinder containing two symmetric collinear radial cracks of equal length with surface elasticity is also solved by using a similar method. The strengths of the logarithmic singularity and the size-dependent torsional rigidity are calculated.     

传导-辐射对沿垂直平面有热泳的瞬时自然对流的影响

研究存在热辐射时,热泳微粒的沉积,对沿垂直平面瞬态自然对流边界层流动的影响,垂直平面浸没在光密灰色流体中.分析中采用Rosseland扩散近似表示辐射热通量项.将控制方程简化为抛物线型的偏微分方程组,然后在整个时间段0≤τ<∞,利用有限差分法数值求解.还得到了小数值时间和大数值时间的渐近解,发现渐近解和数值解吻合很得好.而且,流体,20℃和1个标准大气压下的空气,即Prandtl数Pr为0.7时,用图形给出了不同物理参数,即热辐射参数Rd、表面温度参数θw和热泳参数λ,对瞬时的表面剪切应力τw、表面热传输率qw和组分浓度扩散率(传质率)mw的影响,以及对瞬时的速度、温度和浓度分布曲线的影响.     

三维PTT黏弹性液滴撞击固壁面问题的改进SPH模拟

基于光滑粒子动力学(smoothed particle hydrodynamics, SPH)方法,对三维Phan-Thien Tanner(PTT)黏弹性液滴撞击固壁面问题进行了数值模拟.为了有效地防止粒子穿透固壁,且缩减三维数值模拟所消耗的计算时间,提出了一种适合三维数值模拟的改进固壁边界处理方法.为了消除张力不稳定性问题,采用一种简化的人工应力技术.应用改进SPH方法对三维PTT黏弹性液滴撞击固壁面问题进行了数值模拟,精细地捕捉了液滴在不同时刻的自由面,讨论了PTT黏弹性液滴不同于Newton(牛顿)液滴的流动特征,分析了PTT拉伸参数对液滴宽度、高度和弹性收缩比等的影响.模拟结果表明,改进SPH方法能够有效而准确地描述三维PTT黏弹性液滴撞击固壁面问题的复杂流变特性和自由面变化特征.     

Three-dimensional thermal shock problem of generalized thermoelastic half-space

A three-dimensional model of the generalized thermoelasticity with one relaxation time is established. The resulting non-dimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a specific problem of a half space subjected to thermal shock and traction free surface. The inverses of Fourier transforms and Laplace transforms are obtained numerically by using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the temperature, thermal stress, strain and displacement distributions are represented graphically.     

The flow pattern in a liquid layer and the spectrum of the boundary-value problem when the surface tension depends non-linearly on the temperature

The flow of a liquid in a plane channel on the bottom of which a specified temperature distribution is maintained while the free surface is thermally isolated is considered. The surface tension of the liquid depends quadratically on the temperature. The system of Navier-Stokes and heat conduction equations possess a self-similar solution which leads to the non-linear eigenvalue problem of finding the flow temperature fields in the channel. The spectrum of this problem is investigated analytically for low Marangoni numbers (the second approximation) and numerically in the limiting case of an ideally heat conducting liquid for any Marangoni number. The pattern of the thermocapillary flow in the layer is analysed as a function of the parameter values. The non-uniqueness of the solution, which is typical for problems of this kind, is established. The results are compared with those obtained previously in the first approximation with respect to the Marangoni number.     

A single server model for packetwise transmission of messages

We study a discrete-time single-server queue where batches of messages arrive. Each message consists of a geometrically distributed number of packets which do not arrive at the same instant and which require a time unit as service time. We consider the cases of constant spacing and geometrically distributed (random) spacing between consecutive packets of a message. For the probability generating function of the stationary distribution of the embedded Markov chain we derive in both cases a functional equation which involves a boundary function. The stationary mean number of packets in the system can be computed via this boundary function without solving the functional equation. In case of constant (random) spacing the boundary function can be determined by solving a finite-dimensional (an infinite-dimensional) system of linear equations numerically. For Poisson- and Bernoulli-distributed arrivals of messages numerical results are presented. Further, limiting results are derived.     

An adaptive algorithm in time domain for dynamic analysis of a simply supported beam subjected to a moving vehicle

This paper presents an adaptive algorithm in the time domain for the dynamic analysis of a simply supported beam subjected to the moving load and moving vehicle with/without varying surface roughness. By expanding variables at a discretized time interval, a coupled spatial‐temporal problem can be converted into a series of recursive space problems that are solved by finite element method (FEM), and a piecewised adaptive computing procedure can be carried out for different sizes of time steps. The proposed approach is numerically verified via the comparison with analytical and the Runge–Kutta method‐based solutions, and satisfactory results have been achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

An amphibious vibration-driven microrobot with a piezoelectric actuator

This article concerns microrobots for solid and liquid environments. A short overview of microrobotics, suitable actuators and energy systems is given. The principles of terrestrial and aquatic locomotion are discussed and illustrated with examples from the literature on robotics. The state of the art with a focus on piezo microrobots for solid and liquid environments is presented. Furthermore, we report an amphibious prototype, which can move on flat solid ground and on the free surface of water. The design, characteristic parameters and experiments on locomotion are described. The robot is characterized by a light and simple design and can perform twodimensional locomotion in different environments with a speed up to 30 mm/s. An analytical model to predict the maximum carrying capacity of the robot on water is solved numerically.     

Leveling a capillary ridge generated by substrate geometry

The formation of capillary ridges is typical of thin viscous films flowing over a topographical feature. This process is studied by using a two-dimensional model describing the slow motion of a thin viscous nonisothermal liquid film flowing over complex topography. The model is based on the Navier-Stokes equations in the Oberbeck-Boussinesq approximation. The density, surface tension, and viscosity of the liquid are linear functions of temperature. For a nonisothermal flow over a planar substrate with a local heater, the influence of the heater on the free surface is analyzed numerically depending on the buoyancy effect, Marangoni stresses, and variable viscosity. The analysis shows that the film can create its own ridges or valleys depending on the heater and the dominating liquid properties. It is shown that the capillary ridges generated by the substrate features can be optimally leveled by using various types of heaters consistent with the dominating liquid properties. Numerical results for model problems are presented.     

A moving boundary problem derived from heat and water transfer processes in frozen and thawed soils and its numerical simulation

The seasonal change in depths of the frozen and thawed soils within their active layer is reduced to a moving boundary problem,which describes the dynamics of the total ice content using an independent mass balance equation and treats the soil frost/thaw depths as moving(sharp)interfaces governed by some Stefan-type moving boundary conditions,and hence simultaneously describes the liquid water and solid ice states as well as the positions of the frost/thaw depths in soil.An adaptive mesh method for the moving boundary problem is adopted to solve the relevant equations and to determine frost/thaw depths,water content and temperature distribution.A series of sensitivity experiments by the numerical model under the periodic sinusoidal upper boundary condition for temperature are conducted to validate the model,and to investigate the effiects of the model soil thickness,ground surface temperature,annual amplitude of ground surface temperature and thermal conductivity on frost/thaw depths and soil temperature.The simulated frost/thaw depths by the model with a periodical change of the upper boundary condition have the same period as that of the upper boundary condition,which shows that it can simulate the frost/thaw depths reasonably for a periodical forcing.