Three-dimensional numerical manifold method for heat conduction problems with a simplex integral on the boundary

The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.

A CLASS OF TWO-LEVEL EXPLICIT DIFFERENCE SCHEMES FOR SOLVING THREE DIMENSIONAL HEAT CONDUCTION EQUATION

A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh ratio r = Deltat/(Deltax)(2) = Deltat/(Deltay)(2) = Deltat/(Deltaz)(2) less than or equal to 1/2, which is better than that of all the other explicit difference schemes. And when the order of truncation error is 0((Deltat)(2) + (Deltax)(4)), the stability condition is r less than or equal to 1/6, which contains the known results.

“Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale

Based on constructal theory,the constructs of three "volume-point" heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are optimized by taking minimum entransy dissipation rate as optimization objective.The optimal constructs of the three "volume-point" heat conduction models with minimum dimensionless equivalent thermal resistance are obtained.The results show that the optimal constructs of the three-dimensional cylindrical assembly based on the minimizations of dimensionless equivalent thermal resistance and dimensionless maximum thermal resistance are different,which is obviously different from the comparison between those of the corresponding two-dimensional rectangular assembly based on the minimizations of these two objectives.The optimal constructs based on rectangular and triangular elements on microscale and nanoscale when the size effect takes effect are obviously different from those when the size effect does not take effect.Because the thermal current density in the high conductivity channel of the rectangular and triangular second order assemblies are not linear with the length,the optimal constructs of these assemblies based on the minimization of entransy dissipation rate are different from those based on the minimization of maximum temperature difference.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the construct.The studies on "volume-point" heat conduction constructal problems at three-dimensional conditions and microscale and nanoscale by taking minimum entransy dissipation rate as optimization objective extend the application range of the entransy dissipation extremum principle.

Characteristic finite difference fractional step methods for three-dimensional semiconductor device of heat conduction

The mathematical model of the semiconductor device of heat conduction has been described by a system of four equations. The optimal order estimates in L2 norm are derived for the error in the approximates solution, putting fotward a kind of characteristic finite difference fractional step methods.

电加热防/除冰过程中溢流水再冻结数值模拟

当飞机飞行过程中遇到结冰工况时,为保证飞机的飞行安全以及气动性能,常使用热防护方法作为飞机防除冰的重要手段。本文通过使用共轭耦合方法建立了机翼内部多层导热与水膜流动的耦合计算模型,并针对电加热防除冰过程进行了一系列数值模拟计算。研究选取了可进行非稳态计算的Myers水膜模型,电加热组件导热模型则采用有限体积法隐式离散进行计算,水膜模型与导热模型通过交换边界值的共轭传热方法实现松耦合。研究发现在电加热防除冰过程中,由于积冰融化和水膜流动会产生溢流水再冻结现象。对电加热系统开启后期的积冰外形进行了流场计算与气动分析,发现机翼上下翼面溢流水冻结部位会对流场产生扰动。通过Q准则判断积冰后侧产生了涡结构,对比未发生结冰的干净翼型,机翼前缘位置溢流水冻结导致压力系数曲线发生较大震荡,因此溢流水再冻结问题影响了机翼的气动性能,未能使电加热防除冰系统达到理想的防护效果。

非稳态导热问题分析解特征函数正交性的讨论

非稳态导热问题分析解是传热学中十分重要的内容之一,多数传热学教材对特征函数正交性的论述较为简略,影响了对求解过程的理解.本文以大平板非稳态导热问题分析解求解过程为例,重点讨论了特征函数正交性的含义、特征函数正交性的证明以及特征函数正交性的应用,给出了保持求解过程连贯、帮助学生理解的教学建议,为非稳态导热问题分析解及其数学解析过程的教学提供了参考.

浅埋地下建筑围护结构传热计算方法研究

现有地下建筑围护结构传热计算方法无法较好地与实际工程设计相结合。为对地下建筑围护结构传热计算方法进行优化设计,提出地下建筑围护结构三维非稳态传热计算方法。选取济南市作为寒冷地区典型城市,在MATLAB软件中采用有限容积法进行求解。提出了地下建筑外围墙体名义传热系数的概念,通过大量算例得到三种不同类型地下建筑围护结构在室外设计温度条件下的传热量,并进一步拟合出适合寒冷地区工程设计计算用的传热系数公式。结果表明:各拟合公式均方差r^(2)>0.90,根据计算公式得到的名义传热系数拟合效果良好,能够较好地将浅埋地下建筑传热相关理论与工程实际结合。

转鼓式飞剪大过盈量齿轮的热装与热拆

在大型零件的安装过程中,为了使连接件能输出大的扭矩并能承受大的冲击载荷,过盈配合应用较多。过盈安装比较容易,但是如何拆卸过盈零件,通常比较困难。针对3500 mm炉卷轧机转鼓式飞剪安装过程中同步齿轮热装尺寸不到位,需要将过盈零件调整到正确位置,通过理论计算验证了感应加热的可行性,并最终通过该方法实现了过盈零件的横向移动,不但保护了齿面硬度,而且没有破坏过盈配合面,从实际应用证明了中频感应加热拆除过盈零件方法的可靠性和安全性。利用该方法,成功将2250 mm转鼓式飞剪同步齿轮拆除。

Dynamics of Unsteady MHD Convective Flow with Thermophoresis of Particles and Variable Thermo-Physical Properties past a Vertical Surface Moving through Binary Mixture

The dynamics of unsteady magnetohydrodynamic convective fluid flow with radiation and thermophoresis of particles past a vertical porous plate moving through a binary mixture in an optically thin environment is investigated. The approximate form of the radiative heat flux is considered as the fourth power of temperature. Chemical reaction that occurs as the chemically reacting fluid flow through binary mixture is accounted for in energy and species concentration equations. Exponential space dependent heat source is introduced to generate additional heat energy across the fluid domain. The corresponding influence of heat energy is properly accounted for. It is assumed that viscosity and thermal conductivity vary as a linear function of temperature. The governing boundary layer equations are converted to nonlinear ordinary differential equations using similarity variables. A novel method of obtaining root finding starting with three guesses in shooting techniques is presented. The corresponding nonlinear coupled ordinary differential equations is solved numerically by shooting technique along with quadratic interpolation scheme. Graphical results of the dimensionless velocity, temperature and concentration distributions are shown for certain pertinent parameters controlling the fluid flow. The quadratic interpolation method is found to produce better estimated values of , which satisfy the degree of accuracy and proportional to the physical quantities.

Effect of Heat-Insulating Layer Thickness on Melting Rate of Ice Fixed Abrasives Polishing Pad

The formula of the thickness of the heat-insulating layer is deduced via heat transfer analysis,according to the principle of heat transfer in limited space.Polishing experiments are carried out using the same technological parameters.Compared with the polishing experimental results,the heat transfer model is proved to be correct.As validated by the experimental results,polyurethane heat-insulating layer can effectively improve the service life of the ice fixed abrasive pad and alleviate the melting rate in the polishing process to improve the polishing quality proposed.The heat transfer model provides theoretical basis for research of temperature field of ice fixed abrasive polishing.

Exact Variational Principle For 3-D Unsteady Heat Conduction With Second Sound

The exact variational formulation of the extended unsteady heat conduction equation with finite propagation speed （the 2nd sound speed） of hyperbolic type is derived herein via a systematic and natural way. Moreover, the boundary- and the physically acceptable initial-value conditions are accommodated in the variational principle by a novel method suggested just recently. In this way a perfect justification of the variational theory of transient heat conduction and a rigorous theoretical basis for the finite element analysis of heat conduction are provided.

A BLOCK-CENTERED UPWIND APPROXIMATION OF THE SEMICONDUCTOR DEVICE PROBLEM ON A DYNAMICALLY CHANGING MESH

The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.

基于PHengLEI的非稳态电热除冰过程仿真

为了填补国产自主可控CFD软件风雷平台的防除冰功能开发的空白,本文建立了电热除冰计算模型、计算方法和非稳态导热模型,并在国家数值风洞风雷平台(PHengLEI)基础上,集成了非稳态电热除冰计算和非稳态导热计算功能。通过与主流商业CFD软件仿真结果和实验数据的对比,验证了导热和非稳态电热除冰程序的准确性。针对某飞行工况进行了电热除冰计算,通过对表面溢流水、表面温度、结冰量的计算结果分析,发现合理布局加热片、设计加热热流密度和电热除冰控制率,可实现电热除冰系统的安全运行和能源的高效利用。

日照扁平钢箱梁二维温度场的解析解

针对目前扁平钢箱梁日照作用下温度场的研究方法集中在数值模拟和长期实桥测试,尚未采用解析法研究的现状,根据热传导原理,建立带铺装层的扁平钢箱梁顶板与腹板的温度场模型,利用积分变换法求得二者温度场的解析解。以某独塔斜拉桥为例,重点对比分析顶板温度场实测值与解析解中太阳辐射强度分别采用实测法、Hottle法、幂指数法获得时的计算值,并根据太阳辐射强度采用实测法获得的解析解,进一步探究桥面防撞护栏与钢箱梁断面形式对顶板温度分布的影响。结果表明:在实测法获得的太阳辐射强度下,解析解计算结果与实测值最贴近,其计算值与实测值最大偏差不超过3℃,两者平均绝对误差最大不超过1.3℃;而在幂指数法与Hottle法中,太阳辐射强度采用幂指数法获得时,解析解计算准确度要更高;日照下,桥面防撞护栏遮挡引起的扁平钢箱梁顶板不均匀温度分布主要发生在该护栏附近的顶板位置,且引起的温度不均匀程度与太阳辐射强度呈正相关;PK断面钢箱梁与封闭断面钢箱梁顶板温度分布差异体现在是否开口位置,钢箱梁封闭箱室的保温效果导致箱内外环境温度不同是造成该差异的主要原因。

Three Dimensional Coupling between Elastic and Thermal Fields in the Static Analysis of Multilayered Composite Shells

This new work aims to develop a full coupled thermomechanical method including both the temperature profile and displacements as primary unknowns of the model.This generic full coupled 3D exact shell model permits the thermal stress investigation of laminated isotropic,composite and sandwich structures.Cylindrical and spherical panels,cylinders and plates are analyzed in orthogonal mixed curved reference coordinates.The 3D equilibrium relations and the 3D Fourier heat conduction equation for spherical shells are coupled and they trivially can be simplified in those for plates and cylindrical panels.The exponential matrix methodology is used to find the solutions of a full coupled model based on coupled differential relations with respect to the thickness coordinate.The analytical solution is based on theories of simply supported edges and harmonic relations for displacement components and sovra-temperature.The sovra-temperature magnitudes are directly applied at the outer faces through static state hypotheses.As a consequence,the sovra-temperature description is assumed to be an unknown variable of themodel and it is calculated in the sameway as the three displacements.The final systemis based on a set of coupled homogeneous differential relations of second order in the thickness coordinate.This system is reduced in a first order differential relation system by redoubling the number of unknowns.Therefore,the exponential matrix methodology is applied to calculate the solution.The temperature field effects are evaluated in the static investigation of shells and plates in terms of displacement and stress components.After an appropriate preliminary validation,new benchmarks are discussed for several thickness ratios,geometrical data,lamination sequences,materials and sovra-temperature values imposed at the outer faces.Results make evident the accordance between the uncoupled thermo-mechanical model and this new full coupled thermo-mechanical model without the need to separately solve the Fourier heat conduction relation.Both effects connected with the thickness layer and the related embedded materials are included in the conducted thermal stress analysis.

多层高温作业防护服的导热模型及设计算法

针对高温作业防护服的设计问题,建立了基于傅里叶定律的“外界环境—材料层—空气层—人体皮肤”的非稳态导热模型,给出了适当的初始条件和边界条件,并采用有限差分格式进行离散求解,计算出了高温作业防护服在给定的工作环境条件下,温度的空间分布和时间变化情况。现有的实验数据验证了该模型的有效性。在此基础上,根据二分法完成了热防护服的最优厚度设计,为高温作业防护服的设计提供了合理建议。

基于双层非稳态导热过程的井筒温度场半解析模型

在油气井酸化、压裂增产施工中,温度控制着入井工作液的流变性和酸岩反应速度,是影响裂缝几何形态、酸蚀导流能力和措施后产能的重要因素。但目前的井筒温度场模型还缺乏对非稳态过程的严密推导和精确描述。为此,首先在物性分析的基础上,建立了轴向上离散、径向上解析的双层非稳态导热井筒温度场半解析模型,并通过拉普拉斯变换和Stehfest数值反演方法进行了求解;其次,分析了不同水泥环导热过程处理方法对井筒温度分布的影响,认为假设水泥环具有稳态热阻,模拟输出的误差过大且难以修正;最后,对地层和施工参数进行了敏感性分析,认为岩性、施工排量和注入温度变化对井筒温度分布具有显著的影响,而油管腐蚀的影响则可以忽略。现场实际应用效果表明,该数学模型精度较高,模拟结果与监测结果吻合良好。该成果对于提高单井酸化压裂成功率、增加措施后的产能和油气田采收率具有重要意义。

功率器件散热特性的非稳态测量方法

采用集总参数法对功率器件的散热体系进行了分析,推导了功率器件非稳态导热过程中温度变化的规律,给出了一种通过测量非稳态导热过程中的温度变化曲线确定散热体系特性参数的方法。以模块电源为例,实际测量了在不同状态下电源模块升温及降温过程中的温度变化特性。测试结果与理论预测基本相符,表明这种方法可有效用于工程实际中。该方法不仅可以避免冗繁的计算,且通过实验可方便地测试出功率器件的散热特性,并能够预测其使用过程中的最大温升,尤其适用于散热结构复杂、散热边界条件不易确定的应用场合。

干燥巷道围岩传热对平巷风流温度影响研究

井下巷道中的风流温度受到多种因素的影响,如原岩温度、围岩传热性能、风流与围岩的热交换时间、其他热源等,其中围岩传热起主要作用。为分析围岩传热对风温的影响,以干燥巷道为例,根据巷道围岩与风流热交换规律,通过理论计算,分析水平巷道围岩与风流热交换对风温变化的基本影响规律,为矿井通风设计提供较精确的预测值,使矿井通风设计更精细。

高低温环境下松散煤导热系数研究

为研究冷冻取心过程中煤的温度变化规律,通过在高低温环境下煤体热传导过程中温度变化规律的测试,采用多维非稳态导热的乘积解法,对高低温环境下不同粒径松散煤体导热系数进行理论计算。结果表明,环境温度和松散煤粒度均对煤的温度变化率产生重要影响,不同温度和粒度下煤的导热性能差别较大;煤的比热容和松散煤的导热系数随温度升高而增大,其变化规律可用Polynomial函数表示,而且在同一温度下,松散煤的粒径越大,导热系数也越大。