变系数各向异性热传导问题边界元解法

提出了一种用边界元法求解一般变系数各向异性热传导问题时建立基本解的方法,并导出了求解一般二维和三维各向异性稳态热传导问题的纯边界积分方程。所建立的基本解考虑了热导率是空间坐标的函数,因此所导出的积分方程可用于求解非均质材料传热问题。由热源项引起的域积分,运用径向积分法将其转换成边界积分,形成不需要内部点的纯边界元算法。给出了二维和三维问题3个分析算例,并通过将边界元法结果与有限元法结果进行对比,证明了方法的正确性和有效性。     

圆柱壳开孔应力集中问题的边界元解法

本文将边界元法应用于圆柱壳。在建立积分方程时,作者建议用板的基本解叠加三角级数解作为圆柱壳的基本解,并导出了圆柱壳的边界元解法的基本公式。计算表明,使用该基本解,提高了计算精度。文中还提出了区域积分的处理方法。数值计算显示,用边界元法分析圆柱壳的开孔问题是十分有效的。     

注塑模典型截面温度场的数值分析

通过二维典型截面简化模具的三维结构,建立了注塑模典型截面温度场的边界积分方程,并进行数值求解。将模具温度分为稳态和波动两部分,稳态部分是采用循环平均假设,推导出求解模具典型截面二维稳态温度场的边界积分方程。然后利用边界元法,分别对动模和定模进行传热分析,根据分型面边界相容性条件进行耦合;波动部分是在给出温度波动的微分方程后,利用有限差分法结合传热学对型腔表面温度波动进行数值求解。最后通过实例验证了文中算法的正确性与有效性。     

多场耦合的电磁流量计传感器感生电势计算方法

采用有限元数值计算,对电磁流量计传感器建立三维模型计算空间磁通密度分布。根据权重函数的物理意义从虚电流的定义出发,求得二维权重函数数值解,与解析解基本吻合,并将此法应用于三维权重函数的求解。分别采用二维和三维积分计算磁通密度、权重函数并对流场进行数值耦合,获得电极两端感生电势并与实验值对比,相对偏差分别为-11.8%和-3.9%,证明了所提计算方法的合理性。     

注塑模典型截面温度场的数值分析

通过二维典型截面简化模具的三维结构，建立了注塑模典型截面温度场的边界积分方程。利用边界元法分别对动模和定模进行传热分析，根据分型面边界相容性条件进行耦合，最终求出型腔表面温度场的数值解。通过实例验证了文中算法的正确性与有效性。     

注塑模典型截面温度场的数值分析及影响因素

通过二维典型截面简化模具的三维结构，建立了注塑模典型截面温度场的边界积分方程，并利用边界元法通过分别对动模和定模进行传热分析，根据分型面边界相容性条件进行耦合，最终求出型腔表面温度场的数值解。最后通过实例分析了影响型腔温度的各种因素，也验证了文中算法的正确性与有效性。     

二维弹性问题线性单元边界元法奇异积分问题的处理

采用线性单元的二维弹性问题边界元法具有计算精度高的优点。但当点力所在结点与单元的端结点重合时,出现了奇异积分问题。本工作提出了解决奇异积分问题的一个方法,编制了二维弹性问题线性单元边界元法程序,并给出了两个算例。算例中讨论了角结点附近面力的处理问题。结果表明,本工作编制的边界元法程序是可靠的。     

瞬态热传导方程的SPH法

光滑粒子流体动力学(Smooth Particle Hydrodynamics,SPH)作为一种无网格方法具有无网格、自适应性和拉格朗日性质。本文将SPH方法应用到瞬态热传导问题的求解,通过将二阶导瞬态热传导方程分解成两个一阶导的偏微分方程,同时对时间域进行离散,建立了基于SPH方法的瞬态热传导离散方程。通过镜像粒子法处理边界条件,提高了计算精度。对一维和二维瞬态热传导问题进行数值分析,采用lucy核函数和三次样条核函数进行求解,通过与精确解对比,验证了该方法的可行性和实用性。     

热传导问题的SPH方法及其边界处理

本文将光滑粒子流体动力学（Smooth Particle Hydrodynamics,SPH）方法应用于热传导问题中,通过二阶导的SPH方法求解热传导离散方程。分别采用了镜像粒子法和固定边界粒子法处理SPH方法的边界条件,提高了计算精度;并对不同核函数和不规则边界的热传导问题进行数值模拟,结果表明,二阶导的SPH方法适用于求解热传导问题,并能达到较高的精度和稳定性。     

求解对流扩散问题的积分方程法

提出了一种求解对流扩散问题的积分方程法。在这一方法中,首先利用Laplace方程的级数形式的格林函数将对流扩散方程转化为积分方程,然后利用级数的正交性质,把积分方程进一步简化为代数方程组,求解该方程组即可得到对流扩散方程的级数形式的近似解。最后,分别利用Chebyshev多项式和Fourier级数求解了3个典型的一维和二维对流扩散问题。该方法和有限体积法、有限元法和迎风差分法相比,展现出非常高的精度并且避免了由解的不连续性造成的虚假振荡。     

Linear Heat- and Mass-Transfer Problems: General Formulas and Results

One-, two-, and three-dimensional linear unsteady-state inhomogeneous boundary-value heat- and mass-transfer problems with arbitrary dependences of the equation coefficients on time and on the spatial coordinates are considered. General formulas are obtained that enable one to express the solutions of these problems in terms of the Green function under boundary conditions of all the main types. Integral relations (of the Duhamel integral type) are presented, which allow one to construct the solutions of complex problems on the basis of the solutions of simpler problems. The results obtained can be used in the study of heat and mass transfer in motionless and moving media in the isotropic and anisotropic cases (when bulk and surface chemical reactions occur).     

Heat transfer in layered media with application to oil shale materials

The problem of heat conduction in layered materials has been investigated. Equations for heat conduction developed earlier by Murakami et al. have been used to perform numerical studies for oil shale materials. The resulting solutions are compared to the solutions of the heat equation with effective thermal properties. The comparison yields limits on the validity of using effective medium values of thermal properties for time-dependent problems. The anisotropic nature of heat conduction in layered materials is also studied.     

Axial conduction with boundary conditions of the mixed type

A method is proposed for obtaining nearly analytical solutions to laminar flow thermal entrance region problems with axial conduction when the wall boundary conditions are of the mixed type. The method involves the utilization of Green's functions and the solution of a Fredholm integral equation using the Wiener-Hopf procedure. The method is illustrated by obtaining expressions for the temperature field for laminar flow in a circular tube in the zero Peclet number limit for Robin-Dirichlet wall boundary conditions.     

Exact solutions of nonlinear heat- and mass-transfer equations

The method of generalized separation of variables for solving nonlinear steady and unsteady heat- and mass-transfer equations is outlined. New exact solutions of one-, two-, and three-dimensional heat equations are obtained. Anisotropic media with a nonlinear heat source of general form are considered for the case in which the main thermal diffusivities show a power or an exponential dependence on the spatial coordinates. Equations with a logarithmic heat source are analyzed in detail. The results obtained are applied to the problem of thermal explosion in an anisotropic medium.     

Boundary value problems in transport with mixed and oblique derivative boundary conditions-II: Reduction to first order systems

Mixed second derivative or oblique derivative boundary conditions for the steady state heat conduction equation with heat generation in the two-dimensional plane are of importance in applications[1]. In general, they lead to non-selfadjoint boundary value problems or to singular integral equations.In this paper, the second order partial differential equations have been decomposed into first order systems, which under suitable circumstances can be conveniently adapted to satisfy the mixed or oblique derivative boundary conditions. Furthermore, the differential operator with respect to one of the variables is shown to be symmetric in its domain, possessing a denumerable set of eigenvalues and a complete set of eigenvectors. The solution to the boundary value problems is obtained by expansion in terms of these eigenvectors.The method works in infinite regions with separable coordinates, where it gives the same solution as that by infinite Fourier transform. It also works on finite regions, when periodic boundary conditions are used such as in right circular cylinders. Solutions are presented for an infinite slab and concentric annulus for both mixed and oblique derivative boundary conditions.     

基于红外测温的对流换热系数反识别算法研究

The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.     

Mathematical Modeling of Heat Conduction in Complex-Shaped Bodies by the Boundary Integral Equation Method

A procedure is suggested for modeling heat conduction in complex-shaped bodies by the boundary integral equation method. This procedure is used to calculate the distribution of temperature in a flange of an apparatus with an internal cooling channel.     

Application of the method of weighted residuals to mixed boundary value problems: Dual-series relations

Mixed boundary value problems arise in a number of chemical engineering models for heat conduction, simultaneous diffusion and reaction, and fluid flow whenever there is a change in the type of boundary condition along the same boundary. In this paper a general computer algorithm based on the method of weighted residuals (MWR) is developed for determining approximate solutions of all problems of the above type which lead to dual series equations. The solution procedure reduces the determination of the series coefficients to the solution of a large system of algebraic equations. This technique offers advantages over finite difference or artificial interface methods in the accuracy which can be obtained, the type of problem which may be treated, and the simplicity of calculations to be performed. Solutions obtained by the application of MWR are compared and analysed for three example problems which are of interest in diffusion, reaction and conduction.