稳态圆管导热系数测量装置的预热时间初探

本文分析了稳态圆管法导热系数测量装置预热时间的影响因素,通过对这些因素进行简化处理,给出预测稳态圆管法导数测量装置预热时间的模型。通过和实验比较,本模型可以较好地预测该测量装置的预热时间。     

窑洞拱顶稳态导热的数值研究

冬暖夏凉的被动式窑洞具有重要的研究价值。按窑顶形状可分为半园拱，割园拱，二心园拱等。本文通过对窑顶稳态导热的数值研究，得出不同位置，形状窑顶在内表面处于一，三类边界条件下的导热形态系数和传热系数的计算公式。     

点加热稳态导热系数测量方法研究

针对稳态导热系数测量方法测量过程时间较长、测量装置复杂、以及样品制备和加工工艺复杂等现状,提出了一种新型的点加热稳态导热系数测量方法,构建相应的三维稳态传热物理模型,使加热面温升只与热流密度、样品导热系数和测温点位置相关。通过聚焦连续激光加热样品,缩短样品达稳态时长至分钟量级;建立对照光路消除表面发射率和激光稳定性对温度测量的影响;红外热像仪测量加热表面稳态温度分布,结合物理模型实现导热系数测量。采用多种已知导热系数的标准材料和线性法对测量方法进行验证,并应用该方法测量硅藻土导热系数为0.49～0.60 W/(m·K),误差为6.06%。该方法的测量迅速及非接触特性使其可应用于工程实地测量。     

火用分析在稳态导热中的应用研究

针对平壁一维稳态导热问题开展了研究,通过时间参数τ建立了热流密度Φ与热量Q的函数关系,并对一维平壁稳态导热问题进行模型建立、量化与分析。进而得出火用函数的一般表达式与量化表达式以及以火用参数为基准的导热微分方程式。并且给出了其在实际背景下的应用分析。对导热微分方程式进行了分析,揭示了温差驱动与火用差驱动热量传递的异同,得出火用差驱动对热量传递具有力的效果,更好地体现了驱动力的概念。     

反演高温腔体内壁面温度波动的辐射边界导热反问题

在工业生产中有很多情况需要获得高温腔体内壁温度波动,但在内壁面安装测温装置进行直接测量非常困难,一般通过测量外壁温度再进行反演计算间接获得。而已有反演计算方法未考虑高温壁面与周围环境之间的辐射传热,给反演计算结果带来一定误差,为此建立了考虑辐射边界条件的反演高温腔体内壁面温度波动的导热反问题数学模型,并构造了两组数值试验对数学模型的效果进行检验。计算结果表明,建立的数学模型能够很好的由高温腔体外壁面温度反演得到内壁面温度波动情况。     

非稳态导热方法在能量平衡测试计算中的应用

<正> 一、概述在机械行业能量平衡测试中,往往会遇到一些用于金属材科热处理的电加热设备,如箱式电阻炉、盐浴炉、井式炉等。这些设备在实际使用中,由于受客观因素的限制(一般只允许晚上开炉),炉墙远未达到热稳定状态,为此在计算炉墙温度分布时考虑将被测体系作为非稳定导热系统来计算,通过简化边界条件,     

具有辐射边界的三维非规则域内稳态温度场分析

研究了具有辐射边界的空间非规则域内稳态导热问题,求解方法为在球极坐标系内分离变量,获得级数形式的解后,采用边界离散法确定级数项的待定系数,算例表明,边界离形方法不仅可以解决非正交边界问题,而且也可以处理诸如辐射边界的非线性边值问题。     

三角形肋片非稳态导热数值模拟

采用三角形网格以显式方法对三角形肋片进行了二维非稳态导热数值模拟,结果表明用此种方法来求解可以得到肋片内的二维温度分布,较常用的一维方法精确。同时对三角形肋片相对于其它形式肋片的优点也给予了评价。     

一种二维Stefan反问题的数值求解算法

针对因相变引起边界位置移动的二维Stefan反问题,提出了基于有限体积法(FVM)结合Powell法的求解算法。首先假设待定边界位置的初始猜测值,采用Stefan正问题的无量纲化焓法模型,通过FVM对Stefan正问题进行计算,得到各测温点处对应的温度估计值,计算测量值和估计值的方差,然后采用Powell算法,通过方向置换准则判断搜索正确边界问题的方向向量。通过数值仿真实验对提出的算法进行了验证,讨论了测量误差、测点位置、初值、测量时刻数目以及测点数量对反演精度的影响,并与共轭梯度法(CGM)的反演结果进行了对比。数值实验结果表明,该算法能够精确地识别各种不规则的边界形状,并且对误差和初值等影响因素不敏感,具有良好的稳定性。     

接箍导热系数测试方法研究

本文基于单宗量热物性参数导热反问题理论,对接箍的导热系数进行反演.建立正、反问题模型,利用黄金分割法反演了接箍导热系数,然后用CFD软件模拟了温度场分布,最后分析了测量位置对导热系数反演的影响.研究结果表明,黄金分割法能够适用于单宗量热物性参数的反演,通过测量外表面温度,能够准确地反演隔热油管接箍导热系数.     

Solution of inverse heat conduction problem using the lattice Boltzmann method

In this paper the D2Q9 lattice Boltzmann method (LBM) was utilized for the solution of a two-dimensional inverse heat conduction (IHCP) problem. The accuracy of the LBM results was validated against those obtained from prevalent numerical methods using a common benchmark problem. The conjugate gradient method was used in order to estimate the heat flux test case. A complete error analysis was performed. As the LBM is attuned to parallel computations, its use is recommended in conjugation with IHCP solution methods.     

Solution of inverse heat conduction problem using the Tikhonov regularization method

It is hard to solve ill-posed problems, as calculated temperatures are very sensitive to errors made while calculating “measured” temperatures or performing real-time measurements. The errors can create temperature oscillation, which can be the cause of an unstable solution. In order to overcome such difficulties, a variety of techniques have been proposed in literature, including regularization, future time steps and smoothing digital filters. In this paper, the Tikhonov regularization is applied to stabilize the solution of the inverse heat conduction problem. The impact on the inverse solution stability and accuracy is demonstrated.     

Solution of inverse heat conduction problems using maximum entropy method

A solution scheme based on the maximum entropy method (MEM) for the solution of one-dimensional inverse heat conduction problem is proposed. The present work introduces MEM in order to build a robust formulation of the inverse problem. MEM finds the solution which maximizes the entropy functional under the given temperature measurements. In order to seek the most likely inverse solution, the present method converts the inverse problem to a non-linear constrained optimization problem. The constraint of the problem is the statistical consistency between the measured temperature and the estimated temperature. Successive quadratic programming (SQP) facilitates the maximum entropy estimation. The characteristic feature of the method is discussed with the sample numerical results. The presented results show considerable enhancement in the resolution of the inverse problem and bias reduction in comparison with the conventional methods.     

Solution of the Stationary 2D Inverse Heat Conduction Problem by Treffetz Method

The paper presents analysis of a solution of Laplace equation with the use of FEM harmonic basic functions. The essence of the problem is aimed at presenting an approximate solution based on possibly large finite element. Introduction of harmonic functions allows to reduce the order of numerical integration as compared to a classical Finite Element Method. Numerical calculations conform good efficiency of the use of basic harmonic functions for resolving direct and inverse problems of stationary heat conduction.Further part of the paper shows the use of basic harmonic functions for solving Poisson's equation and for drawing up a complete system of biharmonic and polyharmonic basic functions     

Two dimensional steady-state inverse heat conduction problems

In this work we estimate the surface temperature in two dimensional steady-state in a rectangular region by two different methods, the singular value decomposition (SVD) with boundary element method (BEM) and the least-squares approach with integral transform method (ITM). The BEM method is efficient for solving inverse heat conduction problems (IHCP) because only the boundary of the region needs to be discretized. Furthermore, both temperature and heat flux at the unknown boundary are estimated at the same time. The least-squares technique involves solving the equations constructed from the measured temperature and the exact solution. The measured data are simulated by adding random errors to the exact solution of the direct problem. The effects of random errors on the accuracy of the predictions are examined. The sensitivity coefficients are also presented to illustrate the effect of sensor location on the estimated surface conditions. Numerical experiments are given to demonstrate the accuracy of the present approaches.     

Solution of a stationary inverse heat conduction problem by means of Trefftz non-continuous method

In the paper, the non-continuous FEM with Trefftz base functions (FEMT) applied to direct and inverse problem of heat conduction equation has been presented. For the finite number of base functions in each finite element the temperature field becomes non-continuous on the border between elements. This non-continuity has been decreased with the penalty function added to optimised functional. The numerical entropy distribution and energy dissipation function have been analysed on the common boundaries of elements. Increasing the number of base functions in the finite element substantially decreases the inaccuracies of direct and inverse problem solution.     

Solution to steady-state three-dimensional conduction for a rectangular surface heat source on a semi-infinite body

The solution to the steady-state three-dimensional problem in a semi-infinite body due to a rectangular surface heat source is derived. Some results, in terms of temperature distribution in significant planes, for a rectangular and a square spot are presented. Maximum temperatures as a function of depth and size of the spot are also reported.     

A regularized integral equation method for the inverse geometry heat conduction problem

This paper addresses a new technique for solving the inverse geometry heat conduction problem of the Laplace equation in a two-dimensional rectangle, which, named regularized integral equation method (RIEM), consists of three parts. First of all, the Fourier series expansion technique is used to calculate the temperature field u(x, y). Second, we consider a Lavrentiev regularization by adding a term αg(x) to obtain a second kind Fredholm integral equation. The termwise separable property of the kernel function allows us to transform the inverse geometry heat conduction problem into a two-point boundary value problem and therefore, an analytical regularized solution is derived in the final part by using orthogonality. Principally, the RIEM possesses the following advantages: it does not need any guess of the initial profile, it does not need any iteration and a regularized closed-form solution can be obtained. The uniform convergence and error estimate of the regularized solution u^α(x, y) are proved and a boundary geometry p(x) is solved by half-interval method. Several numerical examples present the effectiveness of our novel approach in providing excellent estimates of unknown boundary shapes from given data.     

A two-dimensional inverse heat conduction problem in estimating the fluid temperature in a pipeline

An inverse heat conduction problem (IHCP) was investigated in the two-dimensional section of a pipe elbow with thermal stratification to estimate the unknown transient fluid temperatures near the inner wall of the pipeline. An inverse algorithm based on the conjugate gradient method (CGM) was proposed to solve the IHCP using temperature measurements on the outer wall. In order to examine the accuracy of estimations, some comparisons have been made in this case. The temperatures obtained from the solution of the direct heat conduction problem (DHCP) using the finite element method (FEM) were pseudo-experimental input data on the outer wall for the IHCP. Comparisons of the estimated fluid temperatures with experimental fluid temperatures near the inner wall showed that the IHCP could accurately capture the actual temperature in form of the frequency of the temperature fluctuations. The analysis also showed that the IHCP needed at least 13 measurement points for the average absolute error to be dramatically reduced for the present IHCP with 37 nodes on each half of the pipe wall.     

A method of fundamental solutions for the radially symmetric inverse heat conduction problem

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric inverse heat conduction problem (IHCP). In the radially symmetric IHCP data on an inner fixed boundary is determined from Cauchy data given on an outer boundary. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach of Johansson et al. (2008) for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.