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.     

Inverse estimation of spatially and temporally varying heating boundary conditions of a two-dimensional object

In many dynamic heat transfer situations, the temperature at the heated boundary is not directly measurable and can be obtained by solving an inverse heat conduction problem (IHCP) based on measured temperature or/and heat flux at the accessible boundary. In this study, IHCP in a two-dimensional rectangular object is solved by using the conjugate gradient method (CGM) with temperature and heat flux measured at the boundary opposite to the heated boundary. The inverse problem is formulated in such a way that the heat flux at heated boundary is chosen as the unknown function to be recovered, and the temperature at the heated boundary is computed as a byproduct of the IHCP solution. The measurement data, i.e., the temperature and heat flux at the opposite boundary, are obtained by numerically solving a direct problem where the heated boundary of the object is subjected to spatially and temporally varying heat flux. The robustness of the formulated IHCP algorithm is tested for different profiles of heat fluxes along with different random errors of the measured heat flux at the opposite boundary. The effects of the uncertainties of the thermophysical properties and back-surface temperature measurement on inverse solutions are also examined.     

Inverse Transient Heat Conduction Problems of a Multilayered Functionally Graded Cylinder

Inverse transient heat conduction problems of a multilayered functionally graded (FG) cylinder are presented. The approach is based on measurement of temperature on the outer surface of the cylinder to estimate the heat flux and convection heat transfer coefficient on its inner surface. The non-Fourier heat transfer equation is employed to accurately formulate the problem. The conjugate gradient method (CGM) is used for the optimization procedure and the incremental differential quadrature method (DQM) is applied to solve the direct, sensitivity, and adjoint problems. The accuracy of the presented approach is examined by simulating the exact and noisy data through different examples. Good accuracy of the obtained results validates the presented approach.     

Two-Dimensional Inverse Heat Transfer Analysis of Functionally Graded Materials in Estimating Time-Dependent Surface Heat Flux

Two-dimensional transient inverse heat conduction problem (IHCP) of functionally graded materials (FGMs) is studied herein. A combination of the finite element (FE) and differential quadrature (DQ) methods as a simple, accurate, and efficient numerical method for FGMs transient heat transfer analysis is employed for solving the direct problem. In order to estimate the unknown boundary heat flux in solving the inverse problem, conjugate gradient method (CGM) in conjunction with adjoint problem is used. The results obtained show good accuracy for the estimation of boundary heat fluxes. The effects of measurement errors on the inverse solutions are also discussed.     

A data method using the inner temperature difference to improve the stability of the inverse heat conduction problems

Abstract

This article proposes a method to construct two series systems for improving the stability of the inverse heat conduction problems (IHCP) in a finite slab. The transfer function between the surface heat flux or temperature and the inner temperature difference is respectively obtained by Laplace transform technique firstly. Then the series systems which can solve IHCP based on the inner temperature difference are constructed by replacing the unsuitable zero and pole points of the transfer function approximated by è approximation. Finally the effects of the series systems are evaluated by a typical example. The results of the evaluation show that this method can obtain the surface heat flux and temperature by the inner temperature difference, and enhance the response speed of the measurement system at the same time. In addition this method can also improve the signal to noise ratio (SNR) of the inverse solutions by selectively amplifying the high SNR parts of the inner temperature difference. The present work provides an effective method to improve the stability of IHCP.     

Boiling heat transfer in vertical minichannels. Liquid crystal experiments and numerical investigations

The paper presents the results of experimental and numerical studies of boiling heat transfer in the flow of refrigerants R123 and R11 through vertical, rectangular minichannels, with one wall heated. An application of liquid crystal thermography has helped detect two-dimensional temperature distribution on the heating surface, allowing determination of boiling heat fluxes and experimental boiling curves. The main objectives of the paper included the development of two-dimensional approach to solve the inverse heat conduction boundary problem for determining local values of internal heating surface temperature, boiling heat flux and heat transfer coefficient, and the improvement of the applied numerical method making use of the equalizing calculus and heating surface temperature measurement errors. A detailed discussion of temperature, heat flux and heat transfer coefficient errors is also provided.     

Monitoring of transient 3D temperature distribution and thermal stress in pressure elements based on the wall temperature measurement

Abstract

Two methods for monitoring the thermal stresses in pressure components of thermal power plants are presented. In the first method, the transient temperature distribution in the pressure component is determined by measuring the transient wall temperature at several points located on the outer insulated surface of the component. The transient temperature distribution in the pressure component, including the temperature of the inner surface is determined from the solution of the inverse heat conduction problem (IHCP). In the first method, there is no need to know the temperature of the fluid and the heat transfer coefficient. In the second method, thermal stresses in a pressure component with a complicated shape are computed using the finite element method (FEM) based on experimentally estimated fluid temperature and known heat transfer coefficient. A new thermometer with good dynamic properties has been developed and applied in practice, providing a much more accurate measurement of the temperature of the flowing fluid in comparison with standard thermometers. The heat transfer coefficient on the inner surface of a pressure element can be determined from the empirical relationships available in the literature. A numerical-experimental method of determination of the transient heat transfer coefficient based on the solution of the 3D-inverse heat conduction problem has also been proposed. The heat transfer coefficient on the internal surface of a pressure element is determined based on an experimentally determined local transient temperature distribution on the external surface of the element or the basis of wall temperature measurement at six points located near the internal surface if fluid temperature changes are fast. Examples of determining thermal and pressure stresses in the thick-walled horizontal superheater header and the horizontal header of the steam cooler in a power boiler with the use of real measurement data are presented.     

Laminar Heat Transfer in a Pipe Subjected to a Circumferentially Varying External Heat Transfer Coefficient

Abstract

Numerical techniques have been used to solve the thermally developed regime for a laminar pipe flow that exchanges heat with a fluid environment in the presence of a circumferentially varying external heat transfer coefficient. By making use of the fact that the temperature distributions have similar shapes at successive streamwise locations, the three-dimensional temperature field was scaled to two dimensions. The resulting two-dimensional eigenvalue problem was solved by a rapidly converging automated scheme that successively refines an initial guess. Solutions were obtained for two circumferential distributions of the external heat transfer coefficient respectively intended to model forced and natural convection cross flows. The circumferential average heat transfer coefficient was found to be quite insensitive to the imposed circumferential variations. The local wall heat flux is nearly circumferentially uniform when the mean value of the external coefficient is high. On the other hand, at low mean values of the external coefficient, the local wall heat flux tends to follow the imposed circumferential variations.     

考虑沸腾和缸内局部传热的缸盖流固耦合传热分析

以某商用车直列6缸柴油机作为研究对象,基于缸内传热模型获得内燃机缸盖和缸套的燃气侧局部传热边界条件;基于均相流沸腾传热模型获得水侧传热边界;实现水侧、燃气侧边界与结构温度场计算的耦合,并判断水腔内沸腾传热的状态。结果表明:缸盖温度计算值与实测值吻合,缸盖最高温度位于缸盖底面两个排气门之间;排气门之间的燃气传热系数和燃气温度均处于较高值,缸内局部传热显著;在缸盖底面中心和排气门附近水腔内的冷却水处于部分发展泡核沸腾状态。     

二维燃烧系统气体发热量的确定

开发了一种求解二维燃烧系统气体发热量和气体温度分布的辐射热负荷反问题的新方法－蒙特卡罗法、共轭梯度法和最小二乘法相结合的方法。讨论了气体吸收系数、固体表面发射率和对流传热系数对反问题计算结果的影响。结果表明，即使测量误差存在，辐射热负荷反问题也能得到较准确的结果。     

Effect of pressure on heat transfer coefficient at the metal/mold interface of A356 aluminum alloy

The aim of this paper is to correlate interfacial heat transfer coefficient (IHTC) to applied external pressure, in which IHTC at the interface between A356 aluminum alloy and metallic mold during the solidification of casting under different pressures were obtained using the inverse heat conduction problem (IHCP) method. The method covers the expedient of comparing theoretical and experimental thermal histories. Temperature profiles obtained from thermocouples were used in a finite difference heat flow program to estimate the transient heat transfer coefficients. The new simple formula was presented for correlation between external pressure and heat transfer coefficient. Acceptable agreement with data in literature shows the accuracy of the proposed formula.     

Non-iterative estimation of heat transfer coefficients using artificial neural network models

The Inverse Heat Conduction Problem (IHCP) dealing with the estimation of the heat transfer coefficient for a solid /fluid assembly from the knowledge of inside temperature was accomplished using an artificial neural network (ANN). Two cases were considered: (a) a cube with constant thermophysical properties and (b) a semi-infinite plate with temperature dependent thermal conductivity resulting in linear and nonlinear problem, respectively. The Direct Heat Conduction Problems (DHCP) of transient heat conduction in a cube and in a semi-infinite plate with a convective boundary condition were solved. The dimensionless temperature-time history at a known location was then correlated with the corresponding dimensionless heat transfer coefficient/Biot number using appropriate ANN models. Two different models were developed for each case i.e. for a cube and a semi-infinite plate. In the first one, the ANN model was trained to predict Biot number from the slope of the dimensionless temperature ratio versus Fourier number. In the second, an ANN model was developed to predict the dimensionless heat transfer coefficient from non-dimensional temperature. In addition, the training data sets were transformed using a trigonometric function to improve the prediction performance of the ANN model. The developed models may offer significant advantages when dealing with repetitive estimation of heat transfer coefficient. The proposed approach was tested for transient experiments. A ‘parameter estimation’ approach was used to obtain Biot number from experimental data.     

A technique for uncertainty analysis for inverse heat conduction problems

A technique is presented for the uncertainty analysis of the linear Inverse Heat Conduction Problem (IHCP) of estimating heat flux from interior temperature measurements. The selected IHCP algorithm is described. The uncertainty in thermal properties and temperature measurements is considered. A propagation of variance equation is used for the uncertainty analysis. An example calculation is presented. Parameter importance factors are defined and computed for the example problem; the volumetric heat capacity is the dominant parameter and an explanation is offered. Thoughts are presented on extending the analysis to include the non-linear problem of temperature dependent properties.     

生物组织热边界条件反演研究

对肿瘤热疗过程中生物组织表面热流及内部温度协同反演进行了研究。首先介绍了激光辐照下生物组织内部光热传输模型，并采用有限体积法和离散坐标法相结合求解生物组织内光热传输问题。然后介绍了模糊推理方法基本原理，并采用改进分散模糊推理方法同时反演了激光诱导肿瘤热疗过程中生物组织表面入射热流及内部温度场。最后分析了热流形式和测量误差对反演结果的影响。结果表明，改进分散模糊推理方法可以准确地同时反演组织表面热流及内部温度分布，并具有较强稳定性和抗误差干扰能力。     

Practical application of inverse heat conduction for wall condition estimation on a rotating cylinder

The solution of the linear, inverse, transient heat conduction problem (IHCP) in a cylindrical geometry is analysed. The rotating cylinder under investigation is experiencing boiling convection induced by the impingement of a water jet. The initial temperature is known, additional temperature measurements in time are taken with sensors positioned at a constant radius within the solid material, and the estimation of the wall heat flux at the external radius is sought. First, simulated temperature measurements inside the cylinder are processed in order to be used to estimate the wall heat flux. When noise is present in the data, some of the simulated results obtained using the least squares method exhibit oscillatory behavior, but these large oscillations are substantially reduced by the implementation of a regularization technique. Real experimental data are also used for the wall condition estimation and for the subsequent building of local boiling curves are plotted and discussed. The question of the possible effect of a temperature dependent conductivity on the reconstructed wall condition is also considered.     

理想流体对流传热问题的理论解

研究理想流体受迫对流传热和自然对流传热问题的理论解。采用流体无垂直于壁面法线方向运动(即无穿透)的条件取代黏性流体在壁面无滑移条件，解决了流体在边界上有滑移时计算对流传热系数的困难，给出了理想流体与平壁受迫对流传热、理想流体与竖直壁面自然对流传热和理想流体在管内受迫对流传热的理论解。结果表明：理想流体的对流传热与黏性流体同样存在着热边界层。在外部流动的情况下，无论受迫对流传热还是自然对流传热，对流传热系数都与流体的导热系数、密度和比热三乘积的二分之一次方成正比。在管内受迫对流的情况下，当无因次长度大于0．05时，局部Nu和界面无因次温度分布都不再变化，对于恒热流边界条件，Nu等于8，截面无因次平均温度等于2；对于恒壁温边界条件，Nu等于5．782，截面无因次平均温度等于2．316。     

Determination of the interfacial heat transfer coefficient h in unidirectional heat flow by Beck's non linear estimation procedure

In the numerical simulation of casting solidification, the thermal behavior of the casting/mold interface is characterized by the interfacial heat transfer coefficient, ‘h’. The determination of h is difficult as it involves the solution of the Inverse Heat Conduction Problem (IHCP). One of the satisfactory solution procedures for solving the IHCP is the Beck's non linear estimation procedure. In this work, this procedure has been used successfully by the authors for the determination of h in steady state unidirectional heat flow.     

AN INPUT ESTIMATION APPROACH TO ON-LINE TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEMS

Abstract

An on-line methodology to solve two-dimensional inverse heat conduction problems (IHCP) is presented. A new input estimation approach based on the Kalman filtering technique is developed to estimate the two separate unknown heat flux inputs on the two boundaries in real time. A recursive relation between the observed value of the residual sequence with unknown heat flux and the theoretical residual sequence of the Kalman filter that assumes known heat flux is formulated. A real-time least-squares algorithm is derived that uses the residual innovation sequence to compute the magnitude of heat flux. This recursive approach facilitates practical implementation, and its capabilities are demonstrated in several typical cases with discontinuous and time-varying heat flux inputs.     

蛋白粉尾气余热回收喷淋塔的热工特性研究

大豆蛋白粉干燥工艺过程产生的高温尾气中蕴含着大量显热和潜热,而无填料、垂直逆流喷淋塔可以深度回收尾气中的余热。对此建立了喷淋塔的数值模型,并通过实验验证其准确性;应用所建模型,分析喷淋高度、入口水温、喷淋密度、尾气流速和尾气入口湿球温度对喷淋塔热回收性能的影响规律,进而获得了喷淋塔在实验工况范围内的换热效率曲线及经验关联式,为尾气喷淋热回收塔的优化设计与工程应用提供了分析工具。     

Development of a distributed-parameter model for the evaporation system in a supercritical W-shaped boiler

In this paper, a distributed parameter model of an evaporation system in a supercritical W-shaped once-through boiler is developed based on the 3-D temperature distribution. The mathematical model was formulated to predict the distributions of the heat flux and the metal-surface temperature while considering a non-uniform distribution of the surface heat transfer and the frictional resistance coefficient. The results show that the heat flux distribution on the front water wall has three high heat flux zones in the W-shaped boiler, and the peak of the heat transfer coefficient moves to the peak of the heat flux gradually with the increment of load at supercritical pressure. The maximum deviation of the metal temperature is nearly 94 °C for different loads. This distributed parameter model is fit for the in-situ operating status of the boiler, and it provides a reference for the heat transfer of a supercritical system.