PRECISE INTEGRAL ALGORITHM BASED SOLUTION FOR TRANSIENT INVERSE HEAT CONDUCTION PROBLEMS WITH MULTI-VARIABLES

IntroductionIHCPs (InverseHeatConductionProblems)arecloselyassociatedwithmanyengineeringaspects,andwelldocumentedintheliteratures,coveringtheidentificationsofthermalparameters[1,2 ],boundaryshapes[3],boundaryconditions[4 ]andsource_relatedterms[5 ,6 ]etc .Howeveritseemsthatonlylittleworkisdirectlyconcernedwithmulti_variablesidentificationsbyauthors’knowledge.Tsengetal.presentedanapproachtodeterminingtwokindsofvariables[7],butonlygavefewnumericalexamplestodeterminethemsimultaneously .Thesol…     

基于遗传算法的一种Tikhonov正则化改进方法

就Tikhonov正则化方法求解第一类算子方程进行了新的探讨,针对展平泛函的极值处理,采用了遗传算法来解决.结合遗传算法的优点,扩大了解决问题的范围.介绍了其基本原理及运算流程,作为此方法的应用,首先对一变截面悬臂梁模型进行截面积反求,另外解决了一个热传导反问题实例,证明了其方法的有效性.     

基于遗传算法的混凝土三维非稳态温度场反分析

大体积混凝土结构施工期间的合理温度控制问题非常重要，而精确进行温度计算所需的一些材料参数往往不易直接测得，需要根据一些易测得的量进行反求。本文基于三维瞬态温度场有限元求解理论与反问题理论，建立了混凝土三维瞬态温度场反问题求解数值模型。运用遗传算法寻求非线性反演问题全局最优解，只需要若干点温度实测值便可实现混凝土多个热学参数如绝热温升、导温、导热系数及热交换系鼓等的同时反演，算例对本文反演方法的反演精度及数值稳定性给出了满意的证明。     

带源参数的二维热传导反问题的无网格方法

利用无网格有限点法求解带源参数的二维热传导反问题，推导了相应的离散方程. 与 其它基于网格的方法相比，有限点法采用移动最小二乘法构造形函数，只需要节点信息，不 需要划分网格，用配点法离散控制方程，可以直接施加边界条件，不需要在区域内部求积分. 用有限点法求解二维热传导反问题具有数值实现简单、计算量小、可以任意布置节点等优点. 最后通过算例验证了该方法的有效性.     

Nucleate and transition boiling in narrow horizontal spaces

Nucleate and transition boiling are performed in a horizontal narrow space between a heated upward-facing copper disk and an unheated surface for saturated n-pentane. The heat flux and the wall temperature are determined by mean of an inverse heat conduction method. The influence of the confinement on the boiling curves and the flow patterns are analysed. Characteristic instabilities are observed at low heat flux and during the transition regime.     

Controlled random search technique for estimation of convective heat transfer coefficient

This paper is concerned with a method for solving inverse heat conduction problem. The method is based on the controlled random search (CRS) technique in conjunction with modified Newton–Raphson method. The random search procedure does not need the computation of derivative of the function to be evaluated. Therefore, it is independent of the calculation of the sensitivity coefficient for nonlinear parameter estimation. The algorithm does not depend on the future-temperature information and can predict convective heat transfer coefficient with random errors in the input temperature data. The technique is first validated against an analytical solution of heat conduction equation for a typical rocket nozzle. Comparison with an earlier analysis of inverse heat conduction problem of a similar experiment shows that the present method provides solutions, which are fully consistent with the earlier results. Once validated, the technique is used to investigate another estimation of heat transfer coefficient for an experiment of short duration, high heating rate, and employing indepth temperature measurement. The CRS procedure, in conjunction with modified Newton–Raphson method, is quite useful in estimating the value of the convective heat-transfer coefficient from the measured transient temperature data on the outer surface or imbedded thermocouple inside the rocket nozzle. Some practical examples are illustrated, which demonstrate the stability and accuracy of the method to predict the surface heat flux.     

三维非稳态热传导逆问题反演算法研究

利用表面温度测量来反演热传导方程中的热源项是一类典型的热传导逆问题,在采用有限体积法对三维非稳态热传导问题进行数值求解的基础上,将该热传导逆问题转化为优化问题,建立了伴随方程法和共轭梯度法这两类反演算法. 采用这两类算法对一个典型算例的计算结果表明:建立的两类反演算法是有效的,具有较好的抗噪性能. 此外,对反演算法中计算收敛准则的选取进行了较深入的分析,结果表明,由于热传导逆问题的不适定性,优化过程中目标函数值越小并不意味着反演结果与真值更为接近,可以通过设定合适的收敛准则来模拟正则化项的作用,克服不适定性的影响.      

Dependence of interfacial heat transfer coefficient on casting surface temperature during solidification of Al–Si alloy castings cast in CO2 sand mold

Interfacial heat transfer coefficient at the metal–mold interface (IHTC) was estimated by an iterative algorithm based on the function specification method. An Al–9 wt% Si alloy plate casting was made in a sand mold prepared by CO₂ process. Thermal history obtained from the experiment was used to solve an inverse heat conduction problem. Acquired transient IHTC values are then given in function of the casting surface temperature at the interface. By comparing the obtained results with previous findings, the influence of grain fineness number and consequently of mold roughness on maximum IHTC values is revealed.     

Nodal predictive error model and Bayesian approach for thermal diffusivity and heat source mapping

This article aims at solving a two-dimensional inverse heat conduction problem in order to retrieve both the thermal diffusivity and heat source field in a thin plate. A spatial random heat pulse is applied to the plate and the thermal response is analysed. The inverse approach is based on the minimisation of a nodal predictive error model, which yields a linear estimation problem. As a result of this approach, the sensitivity matrix is directly filled with experimental data, and thus is partially noisy. Bayesian estimators, such as the Maximum A Posteriori and a Markov Chain Monte Carlo approach (Metropolis–Hastings), are implemented and compared with the Ordinary Least Squares solution. Simulated temperature measurements are used in the inverse analysis. The nodal strategy relies on the availability of temperature measurements with fine spatial resolution and high frequency, typical of nowadays infrared cameras. The effects of both the measurement errors and of the model errors on the inverse problem solution are also analysed.     

共轭梯度法求解非线性多宗量稳态传热反问题

应用共轭梯度法求解非线性多宗量稳态热传导反问题。采用八节点的等参单元在空间上进行离散,建立了便于敏度分析的非线性正演和反演的有限元模型,可直接求导进行敏度分析。给出了相关的数值验证,对测量误差及测点数目的影响作了初步探讨,结果表明,采用的算法能够对非线性稳态热传导中导热系数和边界条件联合反问题进行有效的求解,并具有较高精度。     

Flow and Heat Transfer Through a Polygonal Duct filled with a Porous Medium

The fully developed flow and H1 heat transfer in a polygonal duct filled with a Darcy–Brinkman medium is studied. The efficient method of boundary collocation is used. The problem is governed by the duct shape and a non-dimensional parameter s which characterizes the inverse square root of permeability. Asymptotic formulas for small and large s are derived.     

A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere

In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.     

Heat transfer associated to a hot surface quenched by a jet of oil-in-water emulsion

In hot rolling, the mechanical properties of steel alloys are conditioned by the rolling process but a great part is ensured by the cooling of the hot strip mill. Well controlling this cooling rate and its homogeneity is thus of primary importance for obtaining steels with desired mechanical properties. As the water used in the cooling stage of the rolling process can be polluted by oil (in hot mill strip, some oil is used to lubricate the rolls and a part of it can pollute the water), it is important to know how much varies the cooling rates when water is polluted. In this study, transient cooling has been investigated during quenching of a hot metal disk with various subcooled oil-in-water emulsion jets. The aim of this work is to compare the cooling efficiency of oil-in-water emulsion jet with a pure water jet. Experimental investigations of axisymmetric jet impingements on a preheated hot metal disk (500-600 °C) have been performed with various oil-in-water emulsions. The transient cooling heat fluxes on the quenched side are estimated by coupling the measurement of the temperature field of the other side (rear face) with a semi-analytical inverse heat conduction model.     

Mixed Boundary Value Problem in a Non-homogeneous Medium Under Steady Distribution of Temperature

This paper is concerned with a mixed boundary value problem of a non-homogeneous medium under steady distribution of temperature whose elastic constants are exponential functions of y. By using Fourier cosine transforms the mixed boundary value problem of heat conduction is reduced to a Fredholm integral equation of the second kind. Then the elastic problem of the non-homogeneous semi-infinite half-plane under distribution of load over a plane face is solved. The influence of the non-homogeneity of the material on the thermal stress distribution is illustrated graphically.     

A Novel Method for Uncertainty Inverse Problems and Application to Material Characterization of Composites

A novel method is suggested to deal with so-called uncertainty inverse problems (UIPs) which are a class of inverse problems with uncertainty in the system parameters of the forward model. Interval which represents a closed bounded set of real numbers is used to model and characterize the uncertainty in our formulation, and hence only the bounds of the uncertainty of the system parameters are needed. For a specific input vector, the possible values of the outputs form an interval vector because of the uncertainty. An error function is defined using the measured interval vector of the outputs and those computed using a forward model. The UIP is then formulated as an optimization problem which minimizes the error function. To improve the optimization efficiency, an interval forward model is constructed based on the interval analysis method which can calculate very efficiently the bounds of the outputs caused by the uncertainty of the system parameters. The present method is applied to a complex inverse problem, namely material characterization of composite laminates using elastic waves. Uncertainty of load is considered, and the hybrid numerical method (HNM) is used to compute the transient displacement responses. The engineering constants of two kinds of laminates are successfully identified using the simulated measurements of the outputs.     

Determination of nonuniform heat flux density on boundary in inverse heat conduction problem

This paper develops reducing deviation method to solve inverse heat conduction problem with nonuniform heat flux density on boundary. When the thermocouple is placed a bit far from the boundary, there is no problem on non-convergence in this method. A calculation example is given.     

Modelling of the free surface with heat and mass transfer considerations on a liquid filling a porous slab heated from its sides

The position of the free surface is calculated numerically for a porous slab which is partly filled with a liquid and differentially heated from its sides. A coordinate transformation is used to transform the original problem from a physical coordinate system to a non‐orthogonal system where the free surface becomes a fixed straightline. The transformed problem is then solved using a finite difference method. Results are obtained for Rayleigh numbers up to 1000. The Nusselt numbers increase slightly with medium Rayleigh numbers (convection‐dominated region) as expected. Since at low Ra the conduction is dominant and at high Ra radiation is dominant. Hadizadeh and Tien (Int. J. Heat Mass Transfer 2004; 17 (6):799–804) studied the forced convection on the surface of porous layer. In that paper they dealt with in detail the boundary regime of liquid in the channel and modelled the flow and heat transfer. Copyright © 2007 John Wiley & Sons, Ltd.     

Transient heat-conduction response of a composite plane wall

A method based on the Laplace Transform Technique has been developed to solve the problem of transient one-dimensional heat conduction in a composite plane wall. The temperature distribution is obtained in close form in thes-domain. A series inverse transformation method is used to obtain the temperatures in the time domain. To illustrate the method, it has been applied to evaluate the transient response of three representative composite plane walls.

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Transiente Wärmeleitung einer zusammengesetzten ebenen Wand

Zusammenfassung Hier ist ein auf der Laplace-Transformation basierendes Verfahren entwickelt worden, um das Problem der transienten eindimensionalen Wärmeleitung in einer zusammengesetzten ebenen Wand zu lösen. Die Temperaturverteilung ist durch die geschlossene Form ims-Bereich erhalten worden. Es sind eine Reihe von Transformationsverfahren benutzt worden, um die Temperatur im Zeitbereich zu erhalten. Um das Verfahren zu veranschaulichen, wurde für die Berechnung der transienten Reaktion der drei repräsentativen, zusammengefügten, ebenen Wände angewandt.

     

Comparison of interfacial heat transfer coefficient estimated by two different techniques during solidification of cylindrical aluminum alloy casting

The interfacial heat transfer coefficient (IHTC) is necessary for accurate simulation of the casting process. In this study, a cylindrical geometry is selected for the determination of the IHTC between aluminum alloy casting and the surrounding sand mold. The mold surface heat flux and temperature are estimated by two inverse heat conduction techniques, namely Beck’s algorithm and control volume technique. The instantaneous cast and mold temperatures are measured experimentally and these values are used in the theoretical investigations. In the control volume technique, partial differential heat conduction equation is reduced to ordinary differential equations in time, which are then solved sequentially. In Beck’s method, solution algorithm is developed under the function specification method to solve the inverse heat conduction equations. The IHTC was determined from the surface heat flux and the mold surface temperature by both the techniques and the results are compared.     

Influence of thermophysical properties on the thermal stability of insulated composite superconducting tape

The effect of thermal conductivity and heat capacity on thermal stability of Nb-Ti tape superconductor stabilized with copper and subjected to transient thermal disturbance, was numerically investigated. The problem was solved by using the three- dimensional heat conduction equation. The results show that the anisotropy of thermophysical properties of the superconductor have significant effect on the thermal stability. It is found that the thermal stability of the tape is improved by increasing the heat capacity and decreasing the thermal conductivity. The best limits for anisotrpy factors α _k and α _c are (1.0; 1.5) and (2.0; 2.5), respectively.