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.

A Concise Model and Analysis for Heat-Induced Withdrawal Reflex Caused by Millimeter Wave Radiation

In this study, we consider the heat-induced withdrawal reflex caused by exposure to an electromagnetic beam. We propose a concise dose-response relation for predicting the occurrence of withdrawal reflex from a given spatial temperature profile. Our model is distilled from sub-step components in the ADT CHEETEH-E model developed at the Institute for Defense Analyses. Our model has only two parameters: the activation temperature of nociceptors and the critical threshold on the activated volume. When the spatial temperature profile is measurable, the two parameters can be determined from test data. We connect this dose-response relation to a temperature evolution model for electromagnetic heating. The resulting composite model governs the process from the electromagnetic beam deposited on the skin to the binary outcome of subject’s reflex response. We carry out non-dimensionalization in the time evolution model. The temperature solution of the non-dimensional system is the product of the applied power density and a parameter-free function. The effects of physical parameters are contained in non-dimensional time and depth. Scaling the physical temperature distribution into a parameter-free function greatly simplifies the analytical solution, and helps to pinpoint the effects of beam spot area and applied power density. With this formulation, we study the theoretical behaviors of the system, including the time of reflex, effect of heat conduction, biological latency in observed reflex, energy consumption by the time of reflex, and the strategy of selecting test conditions in experiments for the purpose of inferring model parameters from test data.

具Robin条件的高维扩散方程反问题正则化算法

初始热场和热源同时识别问题是一类热传导方程反问题.通过两个固定时刻的温度测量数据同时反演初始温度和热源项,提出了改进的正则化方法,获得了稳定化算法,给出了正则化参数的选取策略及正则化解的误差估计,对带噪声干扰的测量数据进行预处理以提高数据精度.数值算例验证了算法的有效性.

基于二维热传导方程的COB-LED散热器热模拟

针对COB-LED(Chip on Board-Light Emitting Diode)散热问题,文中基于二维热传导方程建立了一个可快速计算COB-LED散热器表面热分布的数学模型。为了便于模型求解,采用有限差分法求解该数学模型并选择交替方向隐格式作为其差分格式。根据模型中的边界条件和初始条件设计COB-LED常温点亮实验,并基于ANSYS有限元分析软件进行仿真分析。通过比较求解结果、仿真结果和实验结果验证该数学模型的合理性。结果表明,求解结果与实验结果中最高温度相对误差约23.57%,且两者的温度变化趋势一致。求解结果与仿真结果中最高温度相对误差约34.84%,且温度分布较为接近,证明了该数学模型的合理性与正确性。

基于FluxNet的热传导方程反问题的求解器

热传导偏微分方程的求解是工业应用中一种重要的计算,为了解决传统的热传导方程正演运算耗时过长的问题,提出一个基于新型的网络结构FluxNet的求解器。通过热传导方程的正演运算获得关于温度场分布图以及对应的热流密度图的数据集,基于深度学习训练该数据集,建立一个具有卷积层和反卷积层的热流密度网络结构FluxNet模型。使用该求解器预测数据以及实际数据的热流密度图进行测试和验证,实验结果得出该求解器预测的热流密度结构相似度均达到90%以上,达到了工业应用需求。

大跨度斜拉桥钢-混组合梁一维日照温度场高效数值模型构建及试验验证

由于内部材料的分层,钢-混组合梁整体竖向温度梯度分布不均匀,温度场求解困难且模拟精度和效率不理想。该文以傅里叶热传导定律为理论基础,推导了钢-混组合梁的一维日照温度场数值计算通用模型,采用逐次超松弛迭代法进行求解;通过一个钢-混组合梁数值案例,对比分析了该方法与COMSOL的计算精度和效率;基于某大跨度斜拉桥的温度健康监测数据,验证了该方法对于日温度时程和全截面竖向温度梯度仿真的精度,并将竖向温度梯度的仿真结果与我国桥梁规范进行了对比。结果表明:该方法计算精度与物理场仿真软件保持一致,计算效率提升了78.3%,并能准确模拟大跨度斜拉桥钢-混组合梁的竖向温度分布,为大跨度斜拉桥钢-混组合梁温度效应的计算提供了强有力工具。

An analytical model for estimating soil temperature profiles on the Qinghai-Tibet Plateau of China

Soil temperature is a key variable in the control of underground hydro-thermal processes. To estimate soil temperature more accurately, this study proposed a solution method of the heat conduction equation of soil temperature （improved heat conduction model） by applying boundary conditions that incorporate the annual and diurnal variations of soil surface temperature and the temporal variation of daily temperature amplitude, as well as the temperature difference between two soil layers in the Tanggula observation site of the Qinghai-Tibet Plateau of China. We employed both the improved heat conduction model and the classical heat conduction model to fit soil temperature by using the 5 cm soil layer as the upper boundary for soil depth. The results indicated that the daily soil temperature amplitude can be better described by the sinusoidal function in the improved model, which then yielded more accurate soil temperature simulating effect at the depth of 5 cm. The simulated soil temperature values generated by the improved model and classical heat conduction model were then compared to the observed soil temperature values at different soil depths. Statistical analyses of the root mean square error （RMSE）, the normalized standard error （NSEE） and the bias demonstrated that the improved model showed higher accuracy, and the average values of RMSE, bias and NSEE at the soil depth of 10-105 cm were 1.41℃, 1.15℃ and 22.40%, respectively. These results indicated that the improved heat conduction model can better estimate soil temperature profiles compared to the traditional model.

Dynamic Calibration of the Cutting Temperature Sensor of NiCr/NiSi Thin-film Thermocouple

In high-speed cutting, natural thermocouple, artificial thermocouple and infrared radiation temperature measurement are usually adopted for measuring cutting temperature, but these methods have difficulty in measuring transient temperature accurately of cutting area on account of low response speed and limited cutting condition. In this paper, NiCr/NiSi thin-film thermocouples（TFTCs） are fabricated according to temperature characteristic of cutting area in high-speed cutting by means of advanced twinned microwave electro cyclotron resonance（MW-ECR） plasma source enhanced radio frequency（RF） reaction non-balance magnetron sputtering technique, and can be used for transient cutting temperature measurement. The time constants of the TFTCs with different thermo-junction film width are measured at four kinds of sampling frequency by using Ultra-CFR short pulsed laser system that established. One-dimensional unsteady heat conduction model is constructed and the dynamic performance is analyzed theoretically. It can be seen from the analysis results that the NiCr/NiSi TFTCs are suitable for measuring transient temperature which varies quickly, the response speed of TFTCs can be obviously improved by reducing the thickness of thin-film, and the area of thermo-junction has little influence on dynamic response time. The dynamic calibration experiments are made on the constructed dynamic calibration system, and the experimental results confirm that sampling frequency should be larger than 50 kHz in dynamic measurement for stable response time, and the shortest response time is 0.042 ms. Measurement methods and devices of cutting heat and cutting temperature measurement are developed and improved by this research, which provide practical methods and instruments in monitoring cutting heat and cutting temperature for research and production in high-speed machining.

Investigating the thermal conductivity of materials by analyzing the temperature distribution in diamond anvils cell under high pressure

Investigating the thermal transport properties of materials is of great importance in the field of earth science and for the development of materials under extremely high temperatures and pressures.However,it is an enormous challenge to characterize the thermal and physical properties of materials using the diamond anvil cell(DAC)platform.In the present study,a steady-state method is used with a DAC and a combination of thermocouple temperature measurement and numerical analysis is performed to calculate the thermal conductivity of the material.To this end,temperature distributions in the DAC under high pressure are analyzed.We propose a three-dimensional radiative-conductive coupled heat transfer model to simulate the temperature field in the main components of the DAC and calculate in situ thermal conductivity under high-temperature and high-pressure conditions.The proposed model is based on the finite volume method.The obtained results show that heat radiation has a great impact on the temperature field of the DAC,so that ignoring the radiation effect leads to large errors in calculating the heat transport properties of materials.Furthermore,the feasibility of studying the thermal conductivity of different materials is discussed through a numerical model combined with locally measured temperature in the DAC.This article is expected to become a reference for accurate measurement of in situ thermal conductivity in DACs at high-temperature and high-pressure conditions.

温度场的有限差分计算——以一维温度场为例

已有关于温度场的研究多是从热传导方程出发的,且大多未考虑材料性能随温度的变化.从能量平衡的角度研究温度场,能有效考虑热对流边界条件和材料性能随温度变化的问题.为了更好地还原实际情况,首先,基于能量平衡的原理,采用有限差分法建立了瞬态传热问题的有限差分方程;其次,考虑材料性能随温度的变化,使用MATLAB进行编程计算温度场;最后,给出算例,并通过与相应的ABAQUS有限元模拟结果对比,证明该方法能有效处理此类问题.研究发现:在升温环境中,是否考虑材料热工参数随温度变化不影响温度分布规律,但影响温度大小;当考虑材料性能随温度变化时,计算得到的物体内部温度高于不考虑材料性能变化时的温度;环境温度采用国际标准升温曲线时,在边界处物体内部温度变化与环境温度变化形式相同,均呈对数形式;在远离边界的物体内部,温度变化幅度随着离边界距离的增大而减小,温度变化呈指数形式.

锅炉炉渣在冷渣管内的传热特性

基于离散元法,建立并验证了颗粒-颗粒热传导、颗粒-流体-颗粒热传导及颗粒-颗粒热辐射模型,采用温度概率密度函数作为传热效应的评价指标,研究了填充率对冷渣管内高温炉渣颗粒传热的影响。结果表明:填充率降低,料床内颗粒的传热更均匀,高温核缩小的速度更快。传热后期,填充率越小,概率密度函数峰值所对应的量纲一温度越大。不同填充率下,各传热途径所传递的热流量总体上波动不大,颗粒料床内辐射传热传递的热流量占总传热流量的59%,是影响料床内颗粒温度降低的主要因素,其次为颗粒-流体-颗粒热传导(占24%),最后为颗粒间的热传导(占16%)。

多点测温法在煤自燃动力学分析中的应用研究

论文介绍了多种不同的煤自燃实验测试方法,使用多点测温法对煤自燃过程中的活化能进行测定,并在理论和实验上分别与金属网篮法、Chen-CPT(cross points temperature)方法和Jones-HR(heat release)方法进行应用比较分析.结果表明:金属网篮法的实验耗时长、耗材多;Chen-CPT方法受系统的不完全对称影响容易造成结果偏差;Jones-HR方法忽略了试样本身热扩散的影响;多点测温法能够有效规避其他方法的大部分不足之处,其理论模型具有更好的科学性,实验简便易行,结果可信性更高,在煤自燃参数测试中具有良好的适用性.

圆柱体状材料上非Fourier热传导奇异摄动解

运用非Fourier热传导定律在圆柱体状材料上建立温度场模型,该模型在数学上表达为三维奇异摄动双曲方程的初边值问题。首先,通过柱坐标变换,使用奇异摄动方法得到内外解方程;其次,使用分离变量法求解内外解,得到形式渐近解;最后,运用余项估计,得到解的一致有效性。

全自动辐射热传导测试仪的研发

为了研发出操作更方便、测试更准确的辐射热传导测试仪,以辐射热源单元、数据采集单元、运动控制单元、冷却系统单元、安全保护单元为核心,采用以逐次逼近法为基础运算配以数据统计法的专用操作软件,设计了一种全自动辐射热传导测试仪。实现了测试数据自动处理、测试报告自动生成、辐射热源自动校准、辐射热功率智能调节等多项人性化功能。认为:研发的全自动辐射热传导测试仪达到了国外同类仪器水平,减少了人员的劳动量,保证了人员的安全。

中国北方6种常见蕨类植物耐热性研究

利用电导率、半致死温度、细胞伤害率等参数,比较北方6种蕨类植物的耐热性,以期为蕨类植物在北方夏季高温环境园林景观布置中的材料选择提供依据。选择蕨、球子蕨、荚果蕨、粗茎鳞毛蕨、广布鳞毛蕨和中华蹄盖蕨进行耐热胁迫处理,测定叶片相对电导率,使用Logistic方程确定LT50,同时测定蕨类植物的叶表皮结构(叶面积、叶比重、气孔密度)、叶绿素含量、光合特性参数等,分析蕨类植物耐热性与各测定指标之间的相关性,再利用夏季的田间观察数据检验,并结合蕨类植物的地理分布特征,综合评估各试验材料的耐热性。结果表明,温度升高后,测试材料的细胞伤害率呈慢、快、慢的“S”形曲线变化。6种蕨类的高温半致死温度为粗茎鳞毛蕨(63.77℃)>中华蹄盖蕨(62.07℃)>广布鳞毛蕨(61.63℃)>荚果蕨(61.13℃)>球子蕨(58.10℃)>蕨(56.70℃)。田间观察数据与电导率法检测数据基本相符,并与蕨类地理分布特征基本保持一致,LT50可以作为蕨类耐热性的评价依据之一。蕨类叶片的表皮形态指标也可以作为其耐热性的参考。筛选结果可丰富蕨类植物在北京地区园林展示中的应用种类。

城市绿地对北京市热岛强度的影响

针对北京市热岛效应日益加重的问题,提出了基于陆地卫星8号(Landsat8)所携带的陆地成像仪(OLI)和热红外成像仪(TIRS)的Level-1数据反演地表温度、计算植被覆盖度的方法;并构建地表温度反演模型,探究北京市热岛效应与城市绿地面积关系。实验结果表明:高温区大部分集中在中心城区,并向周围的郊区的平原地带呈辐射状扩散,随着城区绿地面积增加,植被覆盖度上升的同时城区的热岛强度也呈下降趋势,说明城市绿地面积的增加与热岛效应呈负相关关系。

混凝土绝热温升和热传导方程的新理论

对不同养护温度条件下的混凝土绝热温升进行了研究 ,并采用化学反应速率来描述时间和温度对混凝土绝热温升的影响 ,探讨了化学反应速率与养护温度之间的关系 .根据混凝土不同养护温度 (4.4℃ ,2 3.3℃和 4 0 .0℃ )时绝热温升试验结果的分析 ,得出如下结论 :(a)混凝土绝热温升可以用三参数双曲线函数描述 ;(b)化学反应速率是混凝土养护温度的非线性函数 ;(c)只有对混凝土样本化学反应速率作进一步研究 。

火灾条件下电缆绝缘失效预测模型研究

通过物理模型简化方法、导热微分方程数值求解、模型输入参数确定等研究,建立了火灾条件下电缆绝缘失效预测模型,并进行模型验证试验。将电缆内部结构简化为一维三层物理模型,给出简化后电缆物理模型内部结构参数计算方法;通过基本假设构建表征电缆内部温度分布的导热微分方程式,建立以混合层热扩散系数、火场环境温度变化和电缆绝缘失效温度为输入参数的电缆绝缘失效预测模型,并给出了模型计算输入参数的确定方法;采用ZR-YJV电缆在SDR-1型电缆热辐射实验炉中开展实验,获得电缆绝缘失效温度、绝缘失效时间和环境温度变化过程;实验结果表明,预测模型计算绝缘失效时间的相对误差较小。

引入多重边界条件的GIS母线温度分布多场耦合计算及影响因素分析

GIS母线温度分布可为触头温度监测及载流能力评判提供参考。基于有限元方法建立实际GIS母线原型的多物理场耦合计算模型,并引入太阳辐射、空气流速、环境温度等多重边界条件,以分析外部气候条件对GIS母线温度分布的影响。开展GIS母线稳态温升实验,验证多重边界下多物理场耦合模型的有效性。基于所建仿真模型,分析负荷电流、环境温度、太阳辐射以及风速对GIS温度分布的影响,结果表明:导体和外壳温度增长率随着负荷增加而逐渐变大;环境温度改变导致GIS温度近似线性变化;太阳辐射导致GIS母线整体温度显著提高,外壳最热点向太阳直射方向偏移,外壳温度展开曲线近似为正弦形;风速导致外壳温度分布偏离正弦形,对导体的降温作用也受到SF6导热能力限制。最后,利用导体温度与GIS外壳最低点温度、环境温度、负荷电流三个条件的数值关系,给出了导体温度的计算方法,与实验值对比表明该方法的精度较高。

蓄热式加热炉钢温预报与炉温优化设定研究

在分析新型蓄热式钢坯加热炉的炉型结构与炉温制度特点的基础上,基于钢坯在炉内受热辐射和钢坯内热传导的机理,设计了二维非稳态导热钢温预报模型,并给出了适用该模型的炉温优化策略.该模型能够对出炉钢坯进行网格化钢温预报,具有精度高,通用性强,能够实现炉内钢坯温度分布的在线预报的特点.仿真研究表明,所提出的炉温优化策略能较大地提高钢坯的加热质量.