热松弛时间对双曲型热传导方程的影响

双曲型热传导方程不遵循传统的傅立叶热传导定律,其传导特性受热松弛时间的影响。确定出双曲型热传导方程的无量纲方程形式,应用有限单元法求解一维瞬态非傅立叶无量纲热传导方程。通过比较,分析不同热松弛时间对非傅立叶热传导过程波动过程和热延迟的影响。     

An analytical study of unsteady heat transfer in the rock surrounding a deep airway

The heat transfer between an airway and the air flowing though it is an unsteady problem. The governing equation of unsteady heat transfer was solved using the method of separation of variables. The solution is an infinite series including Bessel functions. The theoretical solution was analyzed by solving for the positive roots of the transcendental equation by iteration. The dimensionless surface temperature of the surrounding rock is only affected by the Bi number but not by the thermo-physical coefficients of the rock. The dimensionless coefficient of heat transfer, k, decreases with the Fo number similarly to the influence of the Bi number on k. A formula for determining the fully developed stage (FDS) suitable for unsteady heat transfer in the airway is proposed. The FDS from theoretical analysis occurs with Fo from 1.6 to 2. The ratio of excess temperature in the surrounding rock is independent of the initial conditions and only dependent on the Bi number and the relative position in the airway, at the FDS. The calculation error is large when using just the first term from the complete series when Fo is from 2 to 12. Five terms give a solution approximately equal to that found using the complete series. The first term could replace the complete series only when Fo is greater than 12. The FDS plays an important role in predication of the temperature field of the surrounding rock and in simplified calculations.     

非稳态热传导问题的边界元解法

采用与时间无关的基本解和分离变量法,建立了非稳态热传导问题的积分方程、边界积分方程及它们的离散型方程。把复杂的域积分有效地转化为边界积分。给出了几种坐标函数和便于编程的计算格式,并在无参考程序的条件下编制出二维常单元和三维四边形单元的计算程序。     

里兹近似方法与数值方法的比较分析

在系统地介绍里兹变分近似方法的基础上,通过一个直角坐标系和一个圆柱坐标系的算例,对稳态热传导问题进行了计算,同时与数值解和精确解进行比较分析.由此可把近似分析解法用于求解各类复杂的非线性问题.     

对建立球面坐标系中的导热微分方程式探讨

研究球面物体的温度场和导热过程在工程上具有特殊的实用价值。为此,必须运用球面坐标系中导热微分方程式。本文试用微元体法和坐标变换法来建立球面坐标系中导热微分方程式。     

Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective

The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For two cases (body with heat generation and body heated externally) of a solid conducting wall with an open cavity, a dimensionless equivalent thermal resistance based on entransy dissipation definition was taken as the optimization objective to optimize the model constructal geometry. Numerical results validated the necessity and feasibility of the presented method. Comparisons of the numerical results based on minimization of dimensionless maximum thermal resistance and minimization of dimensionless equivalent thermal resistance, respectively, showed that there was no obvious difference between the two results when the volume fraction Φ occupied by cavity was small, but the difference between the two results increased with the increases of Φ and the body aspect ratio H/L for any model. The optimal cavities for bodies heated externally were more slender than those for bodies with heat generation. Heat origin had obvious effect on the global performance of heat transfer. The entransy dissipation of body heated externally increased 2–3 times than that of body with heat generation, indicating that the global performance of heat transfer weakened. The method presented herein provides some guidelines for some relevant thermal design problems.     

磁场淬火瞬态温度场计算机模拟

在前期已提出的热传导方程的基础上，利用相变点附近铁磁材料比热和热膨胀系数的反常现象，建立包含磁场作用的热传导控制方程．应用ANSYS有限元分析软件的热-磁耦合分析功能对中碳钢淬火冷却进行计算机数值模拟分析，定量求解热磁耦合作用下的瞬态温度分布．     

激光加工聚合物微流控芯片暂态烧蚀模型研究

为了预测激光直写加工聚合物微流控芯片三维微流道外形，提出了三维烧蚀加工的解析模型.在CO2激光加工聚合物原理基础上，根据传热学原理和烧蚀面能量守恒原理，建立了激光加工三维暂态烧蚀模型.根据在微元控制面上热传导只发生在表面法向，并且激光加工在瞬时达到准稳态，将三维暂态偏微分方程转化为一维常微分方程.基于烧蚀面上的温度始终保持为降解温度，求出关于激光功率、扫描速度和材料热物理系数的微流道外形函数解，并用聚甲基丙烯酸甲酯进行了实验验证.实验结果表明，由解析模型得到的理论值与实验数据吻合很好，该模型的理论推导是符合实际加工实践的.     

一类反应扩散方程组解的存在惟一性

对一类反应扩散方程组利用变量变换的方法得到与其具有同解性的热传导方程。在一定假设条件下,研究热传导方程解的性质,再南紧性得到满足原假设的解的收敛序列,从而得到热传导方程解的存在性与惟一性。借助于方程与方程组的同解性,最终得到反应扩散方程组解的存在惟一性。     

Existence of positive solutions in a delay logistic difference equation

The author studied the existence of positive solutions of the delay logistic difference equationΔyn=pnyn(1-yτ(n)), n=0,1,2,....where {pn} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)＜n and limn→∞τ(n)=∞. A sufficient condition for the existence of positive solutions of the equation was given.     

蜂窝状陶瓷蓄热体热交换过程的数值模拟

将蜂窝陶瓷蓄热器的热交换方程转化为无量纲量的微分方程．并进行了数值计算。结果表明,对于蜂窝陶瓷蓄热器．其热交换温度效率和热效率,主要受二个无量纲即两个物理量群(无量纲时间、无量纲程度)的约束。通过对这两个物理量群的分析可以得出影响蜂窝陶瓷蓄热器传热效果的各种物理因素。     

一般轴对称非定常热传导问题的有限元分析

目的利用有限元法研究武器身管瞬态热传导问题．方法根据均匀正交各向异性材料轴对称热传导方程及其边界条件,利用变分法及欧拉理论,选取６节点的高精度三角形单元类型,推导了一般轴对称非定常热传导有限元基本方程．并编制了相应的计算程序．结果通过算例分析,从而证实了本套理论及设计程序的正确性及可行性．并就某身管瞬态热传导问题进行了有限元计算．结论该理论及方法对解决一般轴对称非定常热传导问题具有普遍意义．     

Analysis of the effects of the heat of sorption on the process of heat transfer in moisture exchange across a membrane

A theoretical study has been conducted to investigate the effects of mass transfer on heat transfer in moisture exchange across a membrane and a mathematical model describing the heat transfer process with consideration of the heat of sorption was established. A dimensionless variable, Ψ =JLλ /δ (T ₁₀−T ₂₀), which controls the effect of the heat of sorption on the heat transfer in membrane process, was obtained through theoretical analysis, and the effects of Ψ on the heat transfer process were analyzed. Results showed that in the case that the temperature gradient and mass transfer are in the same direction, the effective heat flux changes the direction at Ψ=1. For Ψ<1, the heat transfers from high to low temperature sides through the membrane, and the total thermal resistance increases with increasing the moisture flux across membrane or reducing the temperature difference between the bulk flows on the two sides of membrane. For Ψ>1, the overall effect of the heat and mass transfer is that the effective heat flux points from low to high temperature sides and the total thermal resistance decreases with increasing the mass flux or reducing the temperature difference. In the case that the temperature gradient and mass transfer are in the opposite directions, the existence of the heat of sorption acts to enhance the heat transfer from high to low temperature sides, causing a reduced total thermal resistance, and the greater the mass flux or the smaller the temperature difference, the smaller the total thermal resistance. Supported by the National Natural Science Foundation of China (Grant No. 50576040)     

基于时域边界元法的散热结构瞬态热传导分析

针对散热器结构的瞬态热传导问题,首先,在热力学理论基础上,利用问题的控制方程推导出问题的积分方程;然后针对积分方程中的域积分,采用双互易边界元法(DRBEM)进行处理,得到边界积分方程;再对其进行边界离散,获得常系数微分方程组;最后,运用精细积分法(PIM)进行方程组求解,得到内部点的温度结果.通过边界元法与有限元法计...     

单排水孔轴对称填充流场解析解

工程中通常布置排水孔以降低岩体内部渗流压力.在运行过程中,充填物堵塞排水孔会限制排水能力,威胁工程安全.目前,对于填充排水孔的分析,主要考虑非填充区域的纯流体运动,却鲜有同时考虑填充区域和非填充区域的水流运动.鉴于此,建立自由流-渗流耦合理论模型,分析岩体内轴对称填充排水孔的流速分布,该理论模型中,排水孔中非填充区域纯...     

小样品低温动态传热的行波解

研究了小样品在过冷液氮中快速运动时瞬时动态传热特性．根据双曲型热传输理论推导了该系统中温度场的行波解，结果表明小样品的传热明显遵循波的特性；同时导出了无量纲的冷却速率随热马赫数的增加而增加．说明提高小样品的运动速率有利于提高冷却速率．比较了理论和实验温降曲线，两种曲线的一致性．说明按双曲线模型理论计算小样品的低温动态传热是可行的．     

一维多孔介质热湿耦合传递问题的解析解

为准确确定建筑物的能耗,保证建筑物的使用功能,需对土壤和围护结构中的热湿迁移现象进行研究.本文基于Luikov热湿耦合传递方程,提出了一种计算一维多孔介质瞬态热湿传递的理论分析方法.通过引入无量纲温度、湿度对Luikov方程进行拉普拉斯变换,采用传递函数方法(TFM)得到了一维瞬态热湿传递方程的解析解,该解析解揭示了多...     

基于导热传递函数的球壳体动态导热特性研究

为分析球壳体导热系统的动态导热特性，推导了其导热传递函数的表达式.通过建立球壳体导热系统在球面坐标下的一维物理模型，用拉普拉斯变换法求解了描述其非稳态导热过程的微分方程，并推导出了球壳体的导热传递函数.在不同的边界条件下对球壳体导热传递函数的具体表达式进行了讨论.通过导热传递函数求得了一个具体球壳体系统温度输出与温度激励的振幅比和相位差的表达式，并由此分析了该系统振幅比和相位差随半径以及温度激励频率的变化规律.计算结果表明，利用导热传递函数可以全面表征球壳体的动态导热特性，并为此类导热问题及其反问题的分析和求解提供了新的思路     

Double pull specimen more suitable for measuring bond-slip relationship of FRP-to-concrete interface

A new "conceptual" design named "double pull" specimen was proposed in order to measure the bond-slip (δ-τ) relationship of fiber reinforced polymer (FRP)-to-concrete interface more accurately. A finite element analysis (FEA) was performed for preliminarily evaluating the suitability of the proposed conceptual double pull specimen. Through the FEA, it was indicated that the FRP-to-concrete interface of the proposed conceptual specimen might subject to a much higher load level than that of the most commonly used simple shear specimen, showing a great potential for measuring δ-τ relationship more accurately. In the light of the conceptual specimen, a kind of "practical" double pull specimen was developed and proved to be more suitable for measuring δ-τ relationship through an exploratory experimental study with 20 specimens. Consequently, an experimental program with 10 double pull specimens was performed for measuring the ultimate slip δ_u which was difficult to capture by using the existing specimens. It is shown that the range of δ_u is 0.31-0.52 mm based on the test results. The suggestion for improving the measure method is also put forward.     

Thermal-stress simulation of direct-chill casting of AZ31 magnesium alloy billets

Two-dimensional (2D) transient coupled finite element model was developed to compute the temperature and stress field in cast billets, so as to predict the defects of the I-type billets made from AZ31 magnesium alloy and find the causes and solutions for surface cracks and shrinkages during direct-chill (DC) casting process. Method of equivalent specific heat was used in the heat conduction equation. The boundary and initial conditions used for primary and secondary cooling were elucidated on the basis of the heat transfer during the solidification of the billet. The temperature and the thermal-stress fields were simulated with the thermal-structural coupled module of ANSYS software. The influences of casting parameters on the distributions of temperature and stress were studied, which helped optimize the parameters (at pouring temperature of 680 °C, casting speed of 2 mm/s, heat-transfer coefficient of the second cooling equals to 5 000 W/m²·°C⁻¹). The simulation results of thermal stress and strain fields reveal the formation mechanism of some casting defects, which is favourable for optimizing the casting parameters and obtain high quality billets. Some measures of controlling processes were taken to prevent the defects for direct-chill casting billets. Funded by the 973 National Grand Theoretical Research Program(No. 2007CB613700), the National Sci&Tech Support Program(No. 2007BAG06B04), National Natural Science Foundation of China (No. 50725413), and the Natural Science Foundation of Chongqing(No. CST, 2007bb4413)