AN ANALYTICAL SOLUTION OF HEAT CONDUCTION ON A LOCALLY NONUNIFORMLY HEATED SURFACE OF A PLATE WITH FINITE THICKNESS

In engineering and technology, the following problem is often touched upon A certain portion of a plate with finite thickness is heated on its surface, so that the heat flux along the surface is distributed nonuniformly and varying with time. For this kind of heal conduction, there is no available analytical solution given in existing treatises concerning heat conduction. This paper presents an analytical solution of this problem, its calculation results are in good agreement with the experimental data.

Analytical solutions of transient heat conduction in multilayered slabs and application to thermal analysis of landfills

The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.

Heat Conduction Analytical Solutions to be Applied in Boundary Conditions Obtained from Discrete Data

Analytical solutions have varied uses. One is to provide solutions that can be used in verification of numerical methods. Another is to provide relatively simple forms of exact solutions that can be used in estimating parameters, thus, it is possible to reduce computation time in comparison with numerical methods. In this paper, an alternative procedure is presented. Here is used a hybrid solution based on Green＇s function and real characteristics （discrete data） of the boundary conditions.

Time fractional dual-phase-lag heat conduction equation

We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Laplace and Fourier transforms method. The inverse fractional dual-phase-lag heat conduction problem for the simultaneous estimation of two relaxation times and orders of fractionality is solved by applying the nonlinear least-square method. The estimated model parameters are given. Finally, the measured and the calculated temperatures versus time are compared and discussed. Some numerical examples are also given and discussed.

Explicit analytical solutions of non-Fourier heat conduction equation for IC chip

Four basic explicit analytical solutions of non_Fourier heat conduction equation simulating IC chip thermal condition are derived. Some other analytical series solutions can also be derived with the above_mentioned basic solutions. Analytical solution has its own irreplaceable important meaning in theory. In addition, as the standard solution to check the accuracy, convergence and effectiveness of various numerical computational methods and their differencing schemes, grid generation ways and so on, the analytical solution is very useful also for the newly rapidly developing computational heat transfer.

A Comprehensive Review on Multi-Dimensional Heat Conduction of Multi-Layer and Composite Structures:Analytical Solutions

Heat conduction in multi-layer and composite materials is one of the fundamental heat transfer problems in many industrial applications.Due to different materials types,interface conditions,and various geometries of these laminates,the heat conduction mechanism is more complicated than that of one-layer isotropic media.Analytical solutions are the best ways to study and understand such problems in depth.In this study,different existing analytical solutions for heat conduction in multi-layer and composite materials are reviewed and classified in rectangular,cylindrical,spherical,and conical coordinates.Applied boundary conditions,internal heat source,and thermal contact resistance as the most critical parameters in the solution complexity investigated in the literature,are discussed and summarized in different tables.Various types of multi-layer structures such as isotropic,anisotropic,orthotropic,and reinforced laminates are included in this study.It is found that although more than half a century has passed since the beginning of the research on heat transfer in multi-layer composites,new researches that can help with a better understanding in this area are still being offered.The challenges and shortcomings in this area are also discussed to guide future researches.

ANALYTICAL SOLUTION OF AXIAL SYMMETRICAL WALL TEMPERATURE DISTRIBUTION FOR HOLLOW CYLINDER

Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.

二维慢烤模型点火位置及其温度的理论推演

为理论分析凝聚炸药慢速烤燃过程,并为慢速烤燃点火点位置研究奠定理论基础。根据炸药的热传导理论方程,利用叠加原理和分离变量法,将炸药非反应性热传导项与自热反应热传导项拆分,推导得到凝聚炸药二维慢速烤燃模型的温度分布解析解。计算并分析了自热反应温度场随时间和炸药尺寸的变化规律。根据慢烤试验结果,对理论计算得出的点火点位置、点火温度及时间进行了验证。研究结果表明:理论确定的点火时间、点火点位置与试验测量的点火时间、点火点位置相符。炸药自热反应最高温度所在位置随其尺寸的增加,由中心移动至边缘角落。随着试验时间的增加,自热反应温度分布趋于稳定。就尺寸为∅76×190 mm的RDX炸药而言,发生点火时自热反应温度分布与点火前80000 s时的自热反应温度分布一致。

基于慢烤实验的混合炸药热传导系数计算方法

热传导系数作为炸药的重要热力学参数,显著影响炸药装药的点火响应特性。在未开展炸药热传导系数测定实验的情况下,为了快速有效确定一种新型炸药热传导系数,针对典型圆柱段装药结构,建立了轴对称热传导理论模型,获得混合炸药热传导方程的稳态解析解,提出了基于慢烤实验数据的混合炸药热传导系数计算方法。确定了新型不敏感炸药GOL-1(HMX/Al/AP/Binder)的热传导系数,典型烤燃条件下小尺寸装药结构点火响应数值模拟计算结果显示:不同加热速率下装药中心温升曲线计算结果与实验结果均吻合较好,点火时刻装药中心位置温度和点火时间的计算结果与实验偏差最大为2.27%和1.12%,表明GOL-1炸药热传导系数的有效性及数值模拟方法的可行性。建立的热传导计算方法揭示了慢烤装药温度-时间曲线中包含的炸药导热特性及规律,相比体积加权方法和串/并联导热模型方法更适用于计算混合炸药热传导系数,在缺少新型炸药热传导系数测定实验数据的情况下,不失为一种有效的确定方法,为弹药热安全性设计与评估提供了炸药基础参数,推动安全弹药数字化设计与量化评估发展。

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.

多孔双向功能梯度板瞬态热应力分析

为了研究多孔双向功能梯度板在热荷载作用下的应力变化特征,本文由定解条件结合传热学基本定律得到平面温度场及应力场解析解,运用解析法求解研究模型的应力场,通过算例分析加热时间、沿板长方向的孔隙率控制参数A_(x)、沿板厚方向的孔隙率控制参数A_(y)以及4种边界加热函数对多孔双向功能梯度板热应力分布的影响规律。结果表明:1)板内热应力等高线表现为非对称分布,最大压应力积聚于上边界处且最小压应力积聚于右下区域;2)孔隙率控制参数A_(x)的取值变化不改变板内最大及最小热应力的坐标位置;3)加热时间及孔隙率控制参数A_(y)取值的变化导致板内热应力等高线的变化较大,而孔隙率控制参数A_(x)及上边界加热函数对板内热应力影响作用不显著。

回灌与回扬物理过程的解析推导及灌压变化规律

以回灌过程中渗透系数衰减模型为基础,推导了不同回扬次数的渗透系数解析表达式;将其应用于Theis公式,获得了考虑渗透系数衰减以及暂时性堵塞率条件下回灌与回扬物理过程中含水层压强的解析表达式,更准确地刻画了回灌与回扬的物理机制。计算结果表明:在连续回灌不回扬过程中,井内灌压增长符合指数曲线特征,而采取回扬措施后,由指数连续上升转变为间断式阶梯上升;回扬次数越多,灌压下降越明显,但灌压变化幅度随回扬次数的递增而减小。根据解析解定义的两种堵塞率的结果,可以实现利用实验判断不同成分回灌水源对含水层堵塞机理的分析,从而达到科学制定回灌水源标准的目的。

火灾情况下混凝土板温度场的解析解

针对火灾情况下火场温度和构件边界的温度均随时间不断变化的问题,应用杜哈美尔定理分析了边界温度按一定规律随时间变化的热传导问题。推导得到了火灾情况下混凝土板温度场的解析解公式,并应用MATLAB编程计算得到了解析解结果。比较解析解的计算结果和试验结果发现:两者得到的截面温度场都呈非线性分布;两者的变化趋势一致,即近火面的温度梯度很大,距受火面越远,温度梯度越小;温度曲线都是凸向坐标轴。因此,推导得到的解析解公式适合于求解火灾时混凝土板横截面的温度场。同时,只要能够求出非齐次项与时间无关时的辅助问题的解,便可应用杜哈美尔定理求解该热传导问题的温度场,因此该方法可推广应用于火灾情况下其它构件温度场解析解的计算。

板翅式换热器的动态特性分析解

本文用四个连接矩阵描述多股流换热器通道的连接方式、流体的分流和旁通,获得了多股流换热器及其网络动态特性的通用分析解。应用Pingaud模型对板翅式换热器翅片的动态特性进行简化,从而使该通用解可用来求解多股流板翅式换热器的动态特性。通过计算结果和实验的比较,证明此通用解适用于板翅式换热器动态特性求解。

各向异性木材的热传导

在对空间变量进行变换的基础上,引入木材等效导热系数及其与弦向、径向、顺纹3个主导热系数之间的数量关系,简化了各向异性木材中热传导的非稳态偏微分方程;再应用数学物理方法求解各向异性木材传热过程中温度场时空分布的解析解.

变热物性非定常导热方程的一些显式解析解

各种变热物性（热传导系数、密度与比热为变数）的非定常导热方程的解析解在理论上是有意义的；而且它们对计算传热学也很有实用价值；可以作为标准解来校核各种数值计算以及用来启发发展各种计算技巧例如差分格式、网格生成等等。但已知的解析解很少。本文对直角座标下沿几何座标变热物性的非定常几何一元及二元的导热方程导出了一些代数显式解析解，其中有些解包含有任意函数，其实是无限多个解；可作为发展导热学理论及计算导热学之用．

两相混合材料瞬态导热系统模型偏微分方程组的一个显式解析解

An explicit analytical solution of the differential equation set describing transient heatconduction in mixed two phase materials is derived. Besides theoretical meaning, it canalso be applied to check the accuracy, convergence and effectiveness of various numericalcomputation methods and their differencing schemes, grid generation and so on. The Methodof Variable Separation with Addition to solve partial differential equations prop0sed in thispaper is worth developing further.

热传导方程解的梯度估计和解析性

利用热传导方程初值问题的求解公式,给出了齐次热传导方程初值问题的解是解析函数的证明.对齐次热传导方程的解给出了梯度估计,并通过对各阶偏导数的估计应用泰勒公式,给出了齐次热传导方程的解是解析函数的证明.

球体表面受任意周期热扰动时非傅里叶导热的求解与分析

为研究球体表面遭受任意周期温度变化这类非傅里叶传热情形下的热波传播特性,采用双曲线型热传导方程来描述该超急速热传导问题。首先,利用分离变量法和Duhamel积分原理,得到了球体表面温度突然变化时和以简谐规律周期变化时这两种情况下的解析解;然后,在此基础上应用傅里叶级数展开法和叠加原理,获得了球体表面温度任意周期变化时的非傅里叶热传导的温度场。利用得到的解析表达式进行数值模拟,分析了不同热松弛时间、不同时刻和不同位置对温度响应的影响,讨论了非傅里叶热传导模型所给出的温度响应与傅里叶热传导模型的差别。结果表明:非傅里叶热传导模型所给出的温度响应曲线存在一系列有序的阶跃点,其响应的幅值随着热松弛时间的减小而减小。这种方法能够处理许多在生产实际中具有周期边界条件的非傅里叶热传导问题。

工程热物理学科中的若干解析解

介绍了蔡睿贤给出的工程热物理学科中典型的2组基本方程的解析解,即完全气体无粘可压流动的显式解析解和球体内不定常非Fourier导热的一维代数显式解析解.应用加法分离变量法。