Meshless analysis of three-dimensional steady-state heat conduction problems

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson＇s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method （RKPM）. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.

Voronoi Based Discrete Least Squares Meshless Method for Heat Conduction Simulation in Highly Irregular Geometries

A new technique is used in Discrete Least Square Meshfree（DLSM） method to remove the common existing deficiencies of meshfree methods in handling of the problems containing cracks or concave boundaries. An enhanced Discrete Least Squares Meshless method named as VDLSM（Voronoi based Discrete Least Squares Meshless） is developed in order to solve the steady-state heat conduction problem in irregular solid domains including concave boundaries or cracks. Existing meshless methods cannot estimate precisely the required unknowns in the vicinity of the above mentioned boundaries. Conducted researches are limited to domains with regular convex boundaries. To this end, the advantages of the Voronoi tessellation algorithm are implemented. The support domains of the sampling points are determined using a Voronoi tessellation algorithm. For the weight functions, a cubic spline polynomial is used based on a normalized distance variable which can provide a high degree of smoothness near those mentioned above discontinuities. Finally, Moving Least Squares（MLS） shape functions are constructed using a varitional method. This straight-forward scheme can properly estimate the unknowns（in this particular study, the temperatures at the nodal points） near and on the crack faces, crack tip or concave boundaries without need to extra backward corrective procedures, i.e. the iterative calculations for modifying the shape functions of the nodes located near or on these types of the complex boundaries. The accuracy and efficiency of the presented method are investigated by analyzing four particular examples. Obtained results from VDLSM are compared with the available analytical results or with the results of the well-known Finite Elements Method（FEM） when an analytical solution is not available. By comparisons, it is revealed that the proposed technique gives high accuracy for the solution of the steady-state heat conduction problems within cracked domains or domains with concave boundaries and at the same time possesses a high convergence rate which its accuracy is not sensitive to the arrangement of the nodal points. The novelty of this paper is the use of Voronoi concept in determining the weight functions used in the formulation of the MLS type shape functions.

Meshless Least-Squares Method for Solving the Steady-State Heat Conduction Equation

The meshless weighted least-squares (MWLS) method is a pure meshless method that com- bines the moving least-squares approximation scheme and least-square discretization. Previous studies of the MWLS method for elastostatics and wave propagation problems have shown that the MWLS method possesses several advantages, such as high accuracy, high convergence rate, good stability, and high com- putational efficiency. In this paper, the MWLS method is extended to heat conduction problems. The MWLS computational parameters are chosen based on a thorough numerical study of 1-dimensional problems. Several 2-dimensional examples show that the MWLS method is much faster than the element free Galerkin method (EFGM), while the accuracy of the MWLS method is close to, or even better than the EFGM. These numerical results demonstrate that the MWLS method has good potential for numerical analyses of heat transfer problems.

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.

Unifying quantum heat transfer and superradiant signature in a nonequilibrium collective-qubit system:A polaron-transformed Redfield approach

We investigate full counting statistics of quantum heat transfer in a collective-qubit system constructed by multiqubits interacting with two thermal baths. The nonequilibrium polaron-transformed Redfield approach embedded with an auxiliary counting field is applied to obtain the steady state heat current and fluctuations, which enables us to study the impact of the qubit–bath interaction in a wide regime. The heat current, current noise, and skewness are all found to clearly unify the limiting results in the weak and strong couplings. Moreover, the superradiant heat transfer is clarified as a system-size-dependent effect, and large number of qubits dramatically suppress the nonequilibrium superradiant signature.

Interval finite difference method for steady-state temperature field prediction with interval parameters

A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters.

Numerical Study on Heat Transfer Characteristics of Heated/Cooled Rods Having a Composite Board in between: Effect of Thermal Vias

By placing a sample between a heated and a cooled rod, a thermal conductivity of the sample can be evaluated easily with the assumption of a one-dimensional heat flow. However, a three-dimensional constriction/spreading heat flow may occur inside the rods when the sample is a composite having different thermal conductivities. In order to investigate the thermal resistance due to the constriction/spreading heat flow, the three-dimensional numerical analyses were conducted on the heat transfer characteristics of the rods. In the present analyses, a polymer-based composite board having thermal vias was sandwiched between the rods. From the numerical results, it was confirmed that the constriction/spreading resistance of the rods was strongly affected by the thermal conductivity of the rods as well as the number and size of the thermal vias. A simple equation was also proposed to evaluate the constriction/spreading resistance of the rods. Fairly good agreements were obtained between the numerical results and the calculated ones by the simple equation. Moreover, the discussion was also made on an effective thermal conductivity of the composite board evaluated with the heated and the cooled rod.

On Mechanism of Heat-Conduction and Equation of Thermal Conductivity of Liquid

The recently presented equation for nonequilibrium state of gases is hereextended to liquid,and thus an equation of thermal conductivity for normal liquid is de-rived.The equation is applied to both polar and nonpolar liquids,with the average error of608 experlmental values being 1.75% based upon 110 compounds of 29 types of structures.This method is far better than all the other methods published.

二维稳态热传导方程的无监督自适应激活函数物理信息神经网络方法求解

为了解决传统数值方法的不足,使用神经网络求解偏微分方程成为了数值计算领域的研究热点。以二维稳态热传导方程为例,尝试采用基于无监督学习的传统物理信息神经网络(physics-informed neural network,PINN)方法和自适应激活函数PINN方法求解偏微分方程,讨论采样点选取以及网络结构对PINN方法求解精度的影响。结果表明,PINN可以实现二维稳态热传导方程的无监督学习;在传统PINN方法中引入自适应激活函数加快了二维稳态热传导方程求解的速度;采样点选取相较于网络结构对PINN方法求解精度影响更大。因此,自适应激活函数PINN方法相较于传统PINN方法具有速度更快精度更高的优势。

试算迭代法在求解多层复合材料稳态导热问题中的应用

传热学是能源与动力工程专业类的主干专业基础课之一,在能源与动力工程专业的人才培养方案和课程体系中处于极为重要的地位。教学过程中往往会采用实际工程问题对传热学的知识点进行讲解,使学生对知识点的理解更深刻,而在工程实际问题的求解过程中,常常会用到试算法。本文以通过多层平壁及圆筒壁的稳态导热问题为例,在传热学稳态导热部分的教学中以下两种情况就必须采用试算法:(1)在计算多层平壁稳态导热过程中,各层之间的温度未知导致材料的导热系数无法确定时。(2)在求解通过多层筒壁的稳态导热过程中未知量出现在两个不同的对数中时。此外,在案例探讨的基础上,本文还对迭代过程的收敛性及收敛的加速进行了分析。

水库大坝聚氨酯保温层现场长期服役性能试验研究

为进一步探明水库大坝现场原位聚氨酯保温层长期服役后的劣化特性,以响洪甸水库大坝为例,选取大坝下游面典型部位开展了保温层各层间粘结性能现场试验,采用扫描电镜对现场取样的聚氨酯试样进行了微观形貌表征分析,测试了导热系数、压缩强度等关键性能指标,计算分析了相应的混凝土保温层表面放热系数。聚氨酯层与混凝土基面的拉伸粘结强度以及聚氨酯的压缩性能均有所下降,且潮湿聚氨酯的下降程度远大于干燥聚氨酯。与初始增设聚氨酯时相比,干燥部位聚氨酯保温层因内部微孔结构老化导致其导热系数有所升高(22.9%),但保温服役状态仍满足原设计要求;含水潮湿部位保温层,其保温服役状态已不满足要求。保温层长期服役过程中聚氨酯微孔结构老化与外界水分入侵的耦合作用显著加剧聚氨酯劣化过程,大幅降低其粘结性、压缩性和保温性。

热传导问题的MATLAB数值计算

分析了应用MATLAB中PDE工具箱解热传导问题的方法和步骤 ,编制了三个难以用解析方法求解的算例 .采用有限元法求解导热偏微分方程 ,应用PDE工具箱得到数值解 .对适合圆柱坐标描述的问题 ,通过公式变化将其转换为能用PDE工具箱求解的形式 .算例表明 。

稳态法测量导热系数装置的改进与实验数值计算方法研究

不良导体导热系数的测量普遍采用的是稳态法,表面散热率的间接测量和样品侧面散热与漏热给测量带来一定误差,使得导热系数的实际测量值略微偏大。介绍了新的实验装置和实验方法,并且研究了样品侧面边缘热损失的物理模型,提出了新的数学模型和数据处理方法,纠正了偏差,与实验吻合较好。

组合实心圆柱体热传导瞬态分析的状态变量法

引入状态空间理论,并在时域内应用差分格式,建立了组合实心圆柱体热传导问题的状态方程,对其进行了热传导瞬态分析.为检验该方法的有效性,针对某一给定的初始温度分布给出了精确解答.算例表明,该算法的求解精度较高,对于分析圆柱体的热传导瞬态过程非常有效.同时,该方法还可进一步推广用于叠层圆柱壳的瞬态热应力分析.

MPM复合保温材料导热系数的测定及实验装置的改进

MPM复合材料是一种导热系数较小的保温材料 ,单纯采用石棉作为绝热壁不能克服实验过程中大量的热损失。利用改进护热平板构造出有效的绝热壁的实验装置 ,对 MPM复合保温材料的导热系数进行了实验测试。结果表明 :在所研究的温度范围内该种材料的导热系数与温度呈线性关系 ,即λ=( 2 .0 1 8+ 0 .1 2 2 T)× 1 0 - 2 W· ( m·℃ ) - 1;导热系数的值域说明了此种材料具有较好的隔热保温性能 ;证实了该实验装置误差小于 5 %～ 1 0 %。

层状介质热传导瞬态分析的一种新半数值解法

文章引入状态空间理论,并在时域内应用差分格式,建立了层状介质热传导问题的状态方程,分析了层状介质的热传导瞬态过程;为检验所提方法的有效性,针对一特殊问题给出了其精确解,并将所得结果与精确解做了对比;算例表明,半数值解法的求解精度很高,对于分析层状介质的热传导瞬态过程非常有效;所提方法可进一步推广应用于复合材料层合结构的瞬态热应力的耦合分析。

超磁致伸缩伺服阀用电-机转换器传热及热误差分析

提出了一种超磁致伸缩伺服阀用超磁致伸缩电-机转换器的结构并阐述了其工作原理,此电-机转换器采用了油液冷却和反向补偿法来抑制因热产生的位移输出。为分析温升对超磁致伸缩电-机转换器控制精度的影响,基于导热和对流传热理论建立了其传热模型,给出了稳态时超磁致伸缩棒上的温度和热补偿装置上的温度,分析了冷却油液流速对稳态温度的影响,并采用温度场数值模拟的方法对仿真结果进行了验证。分析结果表明,当控制电流为额定值1 A时,若超磁致伸缩棒和控制线圈间油液速度大于0.1 m/s,热补偿装置和超磁致伸缩棒的温度在20.3℃附近且温差在0.2℃以下。由超磁致伸缩棒和热补偿装置上的温度,进一步推导出了超磁致伸缩电-机转换器因热而产生的误差位移。通过仿真分析得出,在超磁致伸缩棒和控制线圈间油液速度等于0.1 m/s时,棒和外壳温度接近且温升不大,热误差位移不大于0.1μm。

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。

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。