Estimation of the transient surface temperature and heat flux of a steel slab using an inverse method

In the steel industry it is of great importance to be able to control the surface temperature and heating- or cooling rates during heat treatment processes. An experiment was performed in which a steel slab was heated up to 1250 °C in a fuel fired test furnace. The transient surface temperature and heat flux of a steel slab is calculated using a model for inverse heat conduction. That is, the time dependent local surface temperature and heat flux of a slab is calculated on the basis of temperature measurements in selected points of its interior by using a model of inverse heat conduction. Time- and temperature histories were measured at three points inside a steel slab. Measured temperature histories at the two lower locations of the slab were used as input to calculate the temperature at the position of the third location. A comparison of the experimentally measured and the calculated temperature histories was made to verify the model. The results showed very good agreement and suggest that this model can be applied to similar applications in the Steel industry or in other areas where the target of investigation for some reason is inaccessible to direct measurements.     

Identification of wall heat flux for turbulent forced convection by inverse analysis

An inverse problem for turbulent forced convection between parallel flat plates is investigated. The space- and time-dependent heat flux at the upper wall is estimated from the temperature measurements taken inside the flow. In the present study, the conjugate gradient method is adopted for the estimation of the unknown wall heat flux. No prior information is needed for the functional form of the wall heat flux in the inverse analysis. The effects of the measurement errors, the functional form of the wall heat flux, and the location of the sensors on the accuracy of the estimation are investigated. The reconstruction of the wall heat flux is satisfactory when simulated exact or noisy data are input to the inverse analysis. The sensitivity coefficients are discussed in this paper. As expected, it is shown that the accuracy of the estimation can be improved when the sensors are located closer to the upper wall.     

Estimation of heat flux and temperature distributions in a composite strip and homogeneous foundation

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat flux and temperature distributions for the system composed of a multi-layer composite strip and semi-infinite foundation, from the knowledge of temperature measurements taken within the strip. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. Results show that an excellent estimation on the time-dependent heat flux can be obtained for the test case considered in this study.     

Time and space resolved wall temperature and heat flux measurements during nucleate boiling with constant heat flux boundary conditions

The lack of time and space resolved measurements under nucleating bubbles has complicated efforts to fully explain pool-boiling phenomena. In this work, time and space resolved temperature and heat flux distributions under nucleating bubbles on a constant heat flux surface were obtained using a 10 × 10 microheater array with 100 μm resolution along with high-speed images. A numerical simulation was used to compute the substrate conduction, which was then subtracted from the heater power to obtain the wall-to-liquid heat transfer. The data indicated that most of the energy required for bubble growth came from the superheated layer around the bubble. Microlayer evaporation and contact line heat transfer accounted for not more than 23% of the total heat transferred from the surface. The dominant heat transfer mechanism was transient conduction into the liquid during bubble departure. Bubble coalescence was not observed to transfer a significant amount of heat.     

Effect of thermocouple sensor dynamics on surface heat flux predictions obtained via inverse heat transfer analysis

A simple thermocouple model is used in this paper to generate data by simulating the imposition of a triangular heat flux history on a one-dimensional domain. A general inverse heat conduction (IHC) analysis computer program is developed and used to estimate the heat flux history based on the generated data. The results show that the effect of the thermocouple's time constant is to diminish the magnitude of the predicted heat flux history and displace its distribution in time.     

Model for prediction of strip temperature in hot strip steel mill

Proper functioning of set-up models in a hot strip steel mill requires reliable prediction of strip temperature. Temperature prediction is particularly important for accurate calculation of rolling force because of strong dependence of yield stress and strip microstructure on temperature. A comprehensive model was developed to replace an obsolete model in the Western Port hot strip mill of BlueScope Steel. The new model predicts the strip temperature evolution from the roughing mill exit to the finishing mill exit. It takes into account the radiative and convective heat losses, forced flow boiling and film boiling of water at strip surface, deformation heat in the roll gap, frictional sliding heat, heat of scale formation and the heat transfer between strip and work rolls through an oxide layer. The significance of phase transformation was also investigated. Model was tested with plant measurements and benchmarked against other models in the literature, and its performance was very good.     

Estimation of time-dependent heat flux and measurement bias in two-dimensional inverse heat conduction problems

This paper presents the results from the adaptive estimator developed to estimate time-dependent boundary heat flux in two-dimensional heat conduction domain with heated and insulated walls. For the estimation, the algorithm requires only the temperatures measured at the insulated walls. In addition, the estimator also predicts the bias in the measurements. In modeling the system, it is assumed that the input flux and bias sequence dynamics can be modeled by a semi-Markov process. By incorporating the semi-Markovian concept into a Bayesian estimation technique, the estimator consists of a bank of parallel, adaptively weighted, Kalman filters. Computer simulation results reveal that the proposed adaptive estimator has improved estimation performance even for step changing heat flux and measurement bias.     

Two-dimensional inverse problem in estimating heat flux of pin fins

The two-dimensional inverse problem of estimating the unknown heat flux of a pin fin base has been solved using the conjugate gradient method. The advantage of the conjugate gradient method is that no information on the functional form of the unknown quantity is required beforehand. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements of temperature in an interior location of a pin fin. Numerical results show that good estimations on the heat flux can be obtained for all the test cases considered here. Furthermore, such a technique can be applied to determine the heat flux acting on an internal wall surface, where direct measurements are difficult to make.     

Indirect measurement of surface temperature and heat flux: Optimal design using convexity analysis

A method—convexity analysis—is presented for optimizing the design of indirect measurements involving ill-posed inverse heat conduction problems. Convexity analysis yields a concise, quantitative and physically meaningful assessment of any proposed measurement design. One is thus able to make rational design decisions. Typical questions addressed by convexity analysis in inverse heat conduction problems are: What is the best deployment of a given number of measurements? How does the resolution capability deteriorate as the design is altered from the optimum? What is the utility of the marginal measurement—by how much will the resolution improve if an additional measurement is employed? Quantitative answers to these and other design questions are obtained by implementation of an efficient computerizable min-max algorithm. Design optimization by no means replaces the need for interpretational sophistication, but rather ameliorates the analysis of ill-posed inverse problems.     

Inverse problem of estimating the heat flux at the roller/workpiece interface during a rolling process

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space-dependent heat flux at the roller/workpiece interface during rolling process from the knowledge of temperature measurements taken within the roller. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. The results show that an excellent estimation on the space-dependent heat flux can be obtained for the test cases considered in this study.     

Particle Swarm Optimization-based algorithms for solving inverse heat conduction problems of estimating surface heat flux

An inverse analysis of estimating a time-dependent surface heat flux for a three-dimensional heat conduction problem is presented. A global optimization method known as Particle Swarm Optimization (PSO) is employed to estimate the unknown heat flux at the inner surface of a crystal tube from the knowledge of temperature measurements obtained at the external surface. Three modifications of the PSO-based algorithm, PSO with constriction factor, PSO with time-varying acceleration of the cognitive and social coefficients, and PSO with mutation are carried out to implement the optimization process of the inverse analysis. The results show that the PSO with mutation algorithm is significantly better than other PSO-based algorithms because it can overcome the drawback of trapping in the local optimum points and obtain better inverse solutions. The effects of measurement errors, number of dimensionalities, and number of generations on the inverse solutions are also investigated.     

Prediction of protective banks in high temperature smelting furnaces by inverse heat transfer

An inverse phase change heat transfer method has been developed for predicting the time evolution of banks covering the surface of refractory brick walls inside high temperature smelting furnaces. The presence of these banks is indispensable as they serve as a protective barrier against the highly corrosive slag, thereby maintaining the structural integrity of the furnace and prolonging its active life. The numerical model rests on the conjugate gradient solution method with the adjoint equation. It predicts banks thickness and motion relying on the thermal conditions prevailing outside the furnace and temperature measurements taken at one location inside the brick wall. Simulations are carried out to examine the effect of different parameters on the predictive capabilities of the method. Results reveal that the method remains accurate in spite of the fact that the temperature measurements inside the wall are noisy and are taken at depth of few centimetres only. An example showing how the present inverse method can be used to warn on the imminent loss of the protective bank during the operation of a smelting furnace is then provided.     

Thermal stress analysis of a parabolic inhomogeneity under uniform remote heat flux and uniform temperature change

Abstract

We study the distributions of temperature and thermal stresses within a parabolic inhomogeneity when the surrounding matrix is subjected to a system of uniform remote heat flux. Our analysis indicates that: in general, the temperature and the thermal stresses inside the inhomogeneity are linear functions of the two in-plane Cartesian coordinates; and, in particular, the normal stress perpendicular to the axis of symmetry of the parabola is uniform within the inhomogeneity. When the inhomogeneity-matrix system undergoes a uniform temperature change, the normal stress parallel to the axis of symmetry of the parabola is uniform inside the inhomogeneity whereas the other two in-plane stress components are zero inside the inhomogeneity.     

Determination of skin temperature distribution and heat flux during simulated fires using Green's functions over finite-length scales

One of the current practices for measuring heat flux during flash fire testing, forest fires, and other industrial cases focuses on the use of semi-infinite models to predict the heat flux during exposure through surface temperature measurements on simulated skin sensors. For short time frames, these models can be shown to have acceptable accuracy. However, when considering longer time exposures at reduced heat fluxes, such as with firefighters in a forest fire, the accuracy of these models could be brought into question. A one-dimensional, finite length scale, transient heat conduction model was developed using a Green's function approach on a rectangular sensor. The model was developed using transient temperature boundary conditions to avoid the use of complicated radiation and convection conditions at each boundary. For comparison, a semi-infinite model utilizing the same boundary condition on the exposed face was solved using both the Laplace transform method and Green's function method. Experimental data was obtained during exposure to a cone calorimeter. All measurements were taken for a minimum duration of 2 min. This temperature data was used to develop appropriate curves for the boundary conditions and validate the analytical models. It was found that the temperature obtained from the one-dimensional transient heat conduction model based on Green's functions agreed well with the experimental results over longer exposure times, and with reduced error when compared with the semi-infinite model. This suggests that modeling the problem on a finite-length scale will produce more accurate or more conservative temperature and heat flux results over extended periods of exposure in high heat load applications.     

Inverse estimation of heat flux and temperature in multi-layer gun barrel

In this paper, we present an inverse method, an input estimation method, to recursively estimate both the time varied heat flux and the inner wall temperature in the chamber. The algorithm includes the use of the Kalman filter to derive a regression model between the biased residual innovation and the heat flux through a given heat conduction state space model. Based on this regression model, the Recursive Least Squares Estimator (RLSE) is proposed to extract the time-varying heat flux on-line as the input. Computational results show that the proposed method exhibits a good estimation performance and highly facilitates practical implementation.     

Maximum heat flux propagation velocity during quenching by water jet impingement

Maximum heat flux propagation characteristics during quenching of hot cylindrical blocks with initial temperature 250–600 °C have been investigated experimentally using a subcooled water jet. When the wetted area starts moving towards the circumferential region, the heat flux reaches its maximum value and the position of maximum heat flux follows the visible leading edge of the wetting front. If wetting starts immediately after the jet strikes the surface, the velocity of this maximum heat flux point increases with the increase of jet velocity and subcooling and decreases with the increase of block initial temperature. These trends are opposite if there is a long delay before movement of the front.     

Heat flux estimation of a plasma rocket helicon source by solution of the inverse heat conduction problem

A solution of the inverse heat conduction problem (IHCP) by the steepest descent method is carried out in order to determine the waste heat flux from a helicon plasma discharge using transient surface temperature measurements obtained from infrared thermography. The infrared camera data is calibrated against thermocouple data and mapped to real locations on the observed surface. The magnitude and distribution of the heat flux to the gas containment tube in the helicon is investigated as the applied power, gas flow rate, magnetic field distribution and neutral gas are varied.     

Nonlinear inverse heat conduction problem of surface temperature estimation by calibration integral equation method

A calibration integral equation method is proposed for estimating the surface temperature in the context of a nonlinear inverse heat conduction problem. The temperature-dependent thermophysical properties and probe positioning are implicitly accounted in the integral equation formulation through calibration tests. A first kind Chebyshev expansion is applied to represent the temperature-dependent property transform function. The undetermined expansion coefficients associated with the Chebyshev expansion are then estimated through two calibration tests. Regularization of the ill-posed problem is achieved by the future-time method. The optimal regularization parameter is estimated using a phase plane and cross-correlation phase plane analyses. Numerical simulation for stainless steel yields highly favorable surface temperature prediction.     

柴油机活塞在流域换热冷却下的温度场计算分析

活塞作为低速机中承受极高热负荷的重要部件,实现活塞的合理冷却是保证柴油机安全稳定运行的必要手段。为了丰富国内关于低速机活塞复杂冷却腔冷却问题的研究,在借鉴前人研究成果的基础上,进一步分析研究了活塞在动态流域换热冷却下的温度场分布规律。研究发现,活塞的瞬态温度场和稳态温度场分布一致,最低温度均出现在顶面中心,顶面的温度变化趋势与缸内温度场变化规律一致。同时,通过活塞流域分析可知,冷却腔壁面的温度波动主要受冷却流域与壁面对流传热系数值的影响。