Inverse Heat Transfer Problem Research Articles

Three-dimensional ice shape detection based on flash pulse infrared thermal wave testing

Ice detection is an important issue in the field of icing prevention and de-icing. In this study, an experimental platform was built for ice detection using flash pulse infrared thermal wave detection, followed by a quantitative recognition approach for identifying the three-dimensional shape of ice. The new method was combined the edge recognition with thickness calculation of inverse heat transfer problem. And the edge of the ice was based on the Principal Component Analysis (PCA) and the Canny algorithm. Thus, by processing the ice edges and giving an initial thickness, the finite element model of the ice was established to numerically simulate the temperature distribution for ice thickness inversion based on the forward heat transfer problem. Meanwhile, the thickness of the ice was inversed by the Levenberg-Marquardt (LM) method based on the inverse heat transfer problem. The resulting edges and thickness of the ice were found to be in good agreement with the experimental results, demonstrating the feasibility of the proposed methods. This paves the way to explore an effective accurate and quantitative identification method for three-dimensional ice shape detection in infrared thermal wave detection.

A deep learning method for estimating thermal boundary condition parameters in transient inverse heat transfer problem

Estimating thermal boundary condition parameters in the transient inverse heat transfer problem (IHTP) is characterized by instability and non-uniqueness of the solution. This study formulated a simple method based on deep learning, which can realize multi-dimensional real-time prediction of thermal boundary condition parameters. The proposed model combining convolutional neural network (CNN) and long short-term memory networks (LSTM) allowed estimating multiple time-varying parameters based on the time-varying temperature field image of the target. The data-driven model used the computational fluid dynamics (CFD) method to obtain the numerical data, and the influence weight of the parameters was introduced in the training process to improve the generalization ability of the model. An experiment on the cubic cavity was made to verify the reliability of the proposed model to estimate time-varying parameters. The studies we have performed showed that the proposed hybrid models outperformed the standalone models (CNN, LSTM) in estimating multiple time-varying parameters. In the experimental results, the relative errors of air temperature and humidity were only 2.33% and 4.33%, respectively. These attempts of introducing the deep learning method to the IHTP in the present study were successful and it was significant for the study of the transient inverse heat transfer problem.

Stepwise algorithm for estimating intraparticle diffusivity by zero-length-column desorption experiments

There are two problems with intraparticle diffusivity estimation by Zero-length-column (ZLC) desorption experiment: 1) no viable algorithm for producing reliable accuracy estimation, and 2) difficulty in fitting short- and long-term ZLC data to the series solution. To tackle these problems, we propose replacing direct curve-fitting with an algebraic-equation solving followed by a single-parameter curve fitting. This stepwise algorithm uncouples parameters' estimation and facilitates the series-solution fitting. Moreover, the stepwise method can yield from one experimental run multiple parameter estimates, a set of estimates containing the information of random error distribution. This set of estimates provides a direct way of deriving statistics quantifying the parameter-estimation uncertainty, such as variance, standard deviation, confidence interval, etc. The new method was validated by using two independently reported ZLC data sets, and its idea is general and applies to other inverse problems of heat and mass transfer.

Inverse Heat Conduction Problem in Estimating Nuclear Power Plant Piping Performance

Abstract Most of today's operating nuclear plants that were originally designed for 30 or 40-year life are facing the long-term operation issues. Therefore, it is of meaningful importance to assess the time-dependent degradation and the aging of the relevant nuclear systems, structures, and components because of resulting loss of structural capacity. In this framework, the inverse method is implemented starting from temperatures at an accessible boundary, which are measured through a monitoring system. The reconstruction technique uses the elaborated signal provided by the monitoring system to determine temperature at inaccessible surface: this is the so-called inverse heat transfer problem. The inverse space marching method is applied. Analytical and numerical studies are performed taking into account thermal transient conditions in order to determine thermal loads. In particular, the developed code demonstrates to be able to reconstruct temperature and stress profiles in any section of the pipe with a good accuracy. In addition, the thermal loads obtained suggest that the investigated transient condition is not able to jeopardize the integrity of nuclear power plant, confirming the possibility of the plant extension of life.

Enhanced Conjugate Gradient Method for Heat Flux Estimation in Laminar and T-Junction Turbulent Mixing Flow

In this paper, the Jaya algorithm is coupled with the traditional conjugate gradient method (CGM) for solving the inverse heat transfer problem. The coupling of two algorithms is termed as enhanced conjugate gradient method (ECGM). Two different applications have been considered to determine the accuracy and stability of ECGM. First, the algorithm is applied in a steady-state two-dimensional laminar flow through a duct for the boundary heat flux estimation. The accuracy of estimation has been compared with traditional CGM by calculating the root mean square (RMS) error. The ECGM algorithm (RMS =0.142 kW/m2) is found to be more accurate than conventional CGM (RMS = 0.198 kW/m2). ECGM is then applied to determine the peripheral variation of heat flux at the fluid-solid interface of a tube at a section downstream to the T-junction. The experimental temperature readings at the outer periphery of the tube required in the inverse algorithm are simulated by solving the direct heat conduction problem. Here, the heat flux at the fluid-solid interface is obtained by solving the governing equations of the turbulent flow by using commercial computational fluid dynamics software. ECGM is found to be a stable and accurate inverse heat transfer algorithm.

Nature inspired algorithms for the solution of inverse heat transfer problems applied to distinct unsteady heat flux orientations in cylindrical castings

Nature inspired algorithms for the solution of inverse heat transfer problems applied to distinct unsteady heat flux orientations in cylindrical castings

Heat transfer behaviour of funnel mould copper plates with high casting speed during different water supply processes

ABSTRACT In the process of high casting speed, the study of funnel mould (FM) cooling process is particularly important. Based on the copper plate temperature measured by thermocouple, a mathematical model of the inverse heat transfer problem of the thin slab/copper plate was developed to calculate the boundary heat flux, then a positive mathematical model of thin slab/copper plate/cooling water coupled heat transfer has been developed, and the influence of the cooling water flows from top to bottom in the water channels on the heat transfer behaviour of the FM copper plate was analysed. The results show that when the cooling water flows from top to bottom in the water channels was adopted, the peak temperature of the copper plate hot face decreased 117°C, the maximum temperature of the cooling water decreased 24°C. Cooling water velocity and temperature have little influence on heat transfer of copper plate.

Solution to inverse natural convection problem using experimental data

Inverse problems arise in a wide range of practical systems and processes and, thus, form an important and well-known area of research in mathematics and physical sciences. The basic nature of an inverse problem is mathematically ill-posed and, as such, finding a unique, accurate, solution is challenging. A prime example of inverse problems in mechanical engineering is the inverse heat transfer problem where the desired solution is known and the boundary and initial conditions, or even material properties, are not. While the heat conduction problem has attracted the bulk of research due to its generally linear governing physics, inverse heat convection presents a greater challenge. The inclusion of fluid mechanics and the nonlinear nature of momentum and energy equations, combined with the previously mentioned ill-posed nature of the inverse problem, presents a challenging research topic. In this paper, a search-based inverse heat convection methodology, developed earlier, is tested against experimental data. The problem considered is a wall plume flow generated by a heat source, such as an electronic component or a fire, located on a vertical surface. This method shows that by measuring the temperatures at a limited number of points downstream of the heat source, the heat input and location of the source can be estimated within an acceptable range of accuracy. This paper continues the earlier work by including experimental data in the prediction of heat source strength and location. It is shown that the methodology introduced earlier is quite robust and can be used for a variety of important practical applications.

A new multi-objective optimization approach for process parameters optimization during numerical simulation of quenching steel parts

The paper presents the numerical simulation of quenching cylindrical steel sample immersed in three different quenchants: water, 5 % aquatensid solution, and isorapid oil. The quenching process starts from the initial temperature of the cylinder at 850 °C and moves through the air until it reaches the quenching bath. The quenchant is held at constant temperature of 40 °C. The cylinder is made of carefully selected steel which does not change its structure during quenching and heating. Cylindrical samples were manufactured in three different dimensions (R, H), (mm): (12.5 × 100), (25 × 150) and (37.5 × 225), so that four measuring points were installed in each sample. Each measuring point consists of thermocouple installed beneath the cylinder surface, capable of measuring the temperature every half second. Based on the experiment, the numerical simulation is recognized as transient and nonlinear two-dimensional heat conduction problem consisting of the two main tasks: direct heat transfer problem (DHTP) and inverse heat transfer problem (IHTP). The paper proposes a new multi-objective optimization approach for the estimation of heat transfer coefficients during the numerical simulation of quenching cylindrical steel sample. The proposed approach gained better results and less convergence time compared to the results from the literature. The paper includes methods, algorithms and the source code for the calculation of the temperature fields in time and heat transfer coefficient estimation of the IHTP. The simulation software has been implemented in C# programming language and can be found at http://github.com/bhrnjica/quenching_simulation.

The Inverse Heat Transfer Problem of Malan Loess Based on Machine Learning with Finite Element Solver as the Trainer

This paper proposes an efficient neural network both in solving process and time for inverse problem of determining thermophysical parameters of Malan loess. In this work, a finite element method (FEM) model is built for the direct solution of dynamic heat transfer problem in Malan loess, which is used to create the samples for the inverse network. Even more, a horn-like network Parm-Net is established, which takes the nodal temperatures of samples as the input data and the thermophysical parameter as the output data. Besides, the hyperparameters of Parm-Net (the number of neurons, the number of hidden layers, learning rate and batch size) are discussed in detail. Finally, intensive numerical experiments are carried out to demonstrate the effectiveness of our inverse network. The results show that the errors of multiple thermophysical parameters are smaller than the input noise, illustrating that Parm-Net is effective and stable with respect to noisy data.

Solving Inverse Heat Transfer Problems Without Surrogate Models: A Fast, Data-Sparse, Physics Informed Neural Network Approach

Abstract Physics informed neural networks have been recently gaining attention for effectively solving a wide variety of partial differential equations. Unlike the traditional machine learning techniques that require experimental or computational databases for training surrogate models, physics informed neural network avoids the excessive dependence on prior data by injecting the governing physical laws as regularizing constraints into the underlying neural network model. Although one can find several successful applications of physics informed neural network in the literature, a systematic study that compares the merits and demerits of this method with conventional machine learning methods is not well explored. In this study, we aim to investigate the effectiveness of this approach in solving inverse problems by comparing and contrasting its performance with conventional machine learning methods while solving four inverse test cases in heat transfer. We show that physics informed neural network is able to solve inverse heat transfer problems in a data-sparse manner by avoiding surrogate models altogether. This study is expected to contribute toward a more robust and effective solution for inverse heat transfer problems. We intend to sensitize researchers in inverse methods to this emerging approach and provide a preliminary analysis of its advantages and disadvantages.

Effect of geological stratification on estimated accuracy of ground thermal parameters in thermal response test

The ground thermal properties are the basic parameters for the design of borehole heat exchanger (BHE) in ground–coupled heat pump system (GCHPs), and their accuracy directly affects the economy and reliability of the heat pump system. In traditional design, ground is usually regarded as an isotropic homogeneous medium, and its thermal properties are obtained by solving the inverse heat transfer problem in BHE through in-situ thermal response test (TRT). In fact, different geological layers can be observed along the depth of BHE, and thermal physical properties of each layer are different based on the ground geological conditions. In order to investigate the effect of geological stratification on estimated accuracy of ground thermal parameters in TRT, a validated numerical layered BHE model (NLBM) is presented to simulated TRT, and the fluid temperature response is used to estimate effective ground thermal conductivity and borehole thermal resistance based on line source model (LSM). Secondly, the distributions of fluid temperature in U-pipe and heat flux of BHE along the depth are compared and analyzed based on the NLBM and the numerical homogeneous BHE model (NHBM). At last, borehole thermal resistance from the NLBM and estimated borehole thermal resistance from LSM are compared. The results show the maximum heat flux in the 3rd layer of the NLBM is 21.1% higher than that of NHBM, and the minimum heat flux in the 1st layer is reduced by 46.9% in the 100 h duration. The estimated λLSM using the fluid temperature responses in the NLBM is 1.3% higher than the thickness-weighted thermal conductivity in the NLBM. The minimum relative error between RLSM and Rb is still up to 10.45% in the duration of 100 h even though extending the duration is helpful to improve the estimated accuracy of RLSM.

Physics-Assisted Deep Neural Network for Inverse Unsteady Heat Transfer Problems

Physics-Assisted Deep Neural Network for Inverse Unsteady Heat Transfer Problems

Analysis of the Influence of Boundary Condition on Simulation Accuracy of Solidification Thermokinetics Model

For a sample steel casting of a cylindrical shape that was cast in a metallic cylindrical mould, the analysis of influence and importance of the main boundary condition on the simulation accuracy of the temperature field in the system of casting-mould-environment was performed. For this system, the influence of the boundary condition on the frame of the mould, on the bottom of the mould, on the top of the casting, and on the casting-mould interface was analysed. As a comparing quantity for accuracy, the time-dependent temperature field (by means of isotherms) of the casting and of the mould and the total solidification time were selected. When the simulation considers the boundary conditions of one of these boundaries of the system, the heat transfer coefficient on the remaining three boundaries of the system is equal zero. The resultant heat flow along the axis is zero always. The conclusions can be used for fine-tuning of solidification models as well as for other applications; e.g. analysis and solution of inverse heat transfer problems.

Methodology for Determining the Thermal and Thermal-Stress States of a Concrete Storage Container for Spent Nuclear Fuel for Assessment of Its Service Life

The work is devoted to the development of methodologies for determining the thermal and thermal-stress states of the main equipment in dry container storage facilities for spent nuclear fuel. Storage facilities of this type are most common for spent fuel of nuclear power reactors. The safety of storage equipment in terms of assessing its service life is not covered widely enough in the world scientific literature. In particular, there are no effective methods for calculating the thermal and thermal-stress states of the equipment that would take into account the influence of many external factors throughout the life of a storage facility. To assess the thermal state of the containers, forward conjugate heat transfer problems, accounting for the mutual heat transfer in both a solid body and in the fluid environment (air), are proposed to be solved. Based on the solution of the conjugate heat transfer problems, the boundary conditions are to be determined to further assess the thermal-stress state of storage containers using inverse heat transfer problems. The proposed approach to determining the thermal and thermal-stress states of a concrete spent fuel container will promote more effective methods for assessing the service life of dry spent fuel storage facilities, which is, in turn, necessary in the development of ageing management programs for storage equipment and long-term safe operation.

THERMOPHYSICAL CHARACTERISTICS OF THE HEAT AND MASS TRANSFER EQUATION IN SOIL

The paper presents the coefficient inverse problem of heat and mass transfer. It is known that the process of moisture and heat transfer in soil is described by a system of partial differential equations. The inverse coefficient problem is solved for finding the thermophysical characteristics of the heat and mass transfer equations. The initial-boundary conditions for the heat and mass transfer system are set. To solve the problem, the measured values of temperature and moisture are additionally set at the accessible boundary of the considered area. To solve the inverse problem, the Dufort- Frankel scheme and Matlab Optimization Toolbox are used. The Jacobian is used to reduce the number of iterations. The results of numerical calculations with and without Jacobian are presented.

Non-contact heat transfer models identification for laser hyperthermia of semi-transparent materials

The identification of mathematical models of heat transfer traditionally involves the installation of temperature sensors inside the sample under study and registration of the response to external thermal effects. In cases where the use of contact methods for measuring temperature is impossible, it is necessary to develop new approaches to determining the unknown thermophysical and radiation-optical characteristics. Laser hyperthermia of superficial tissues is one such case. The paper proposes a method for identifying a model of one-dimensional unsteady heating of a semitransparent sample using non-contact thermometry. A feature of the physical process under consideration is the possibility of its discretization. Due to this, a two-stage iterative procedure for solving the inverse heat transfer problem was formulated. The implementation of the proposed algorithm using software made it possible to carry out a computational experiment. The results showed the effectiveness of this approach. The presented method can be used in the development of means for monitoring and regulating the laser hyperthermia procedure.

Robustness and Accuracy of the Particle Swarm Optimisation Method in the Solution of Inverse Heat Transfer Problems with Phase Change

Some engineering heat transfer problems cannot be solved directly as certain parameters influencing heat transfer are unknown. This is where the solution of inverse heat transfer problems might be utilized. The paper explores application of the Particle Swarm Optimisation (PSO) method to heat transfer problems with phase change. In order to assess the robustness and accuracy of the method, the study was conducted on simulation results. The explored case is an air-PCM heat exchanger. In the first step, the simulations with various values of parameters influencing heat transfer were performed. All cases were simulated as transient with time-dependent boundary conditions. In the second step, some of these parameters (phase change temperature, density, thermal conductivity, etc.) were assumed to be unknown and they were obtained from the simulation results with the use of the PSO method. The cost function was defined in the form of a root mean square error between the simulation results (the outlet air temperature from the heat exchanger) and the results of the optimized scenario. The number of unknown parameters varied from one to seven (in case of the description of the relationship of effective heat capacity on temperature, which was parameterized in the form of an asymmetric Gaussian function). The results have shown that the PSO is a robust and accurate tool with only up to 2 % difference in the enthalpy of fusion and no significant discrepancies during the higher dimension optimisation.

Attitude Determination System of Spacecraft Based on the Inverse Heat Transfer Problems

A reliable control of current orientation of a spacecraft is a critical task in aerospace engineering, as the loss of the spacecraft’s attitude can endanger the whole mission. This makes it important to elaborate on a reliable and robust attitude control system of a spacecraft, which can extend its lifetime. It must have a simple design, and low mass and power consumption. To develop it, we use various conditions of radiative heating at the surface of the spacecraft’s elements with different directions to the Sun and a planet that a satellite orbits to estimate their angular position. In the case of slow angular velocity of a spacecraft, temperature measurements can be used to estimate integral (over the spectrum) radiative flux using specially designed thermal sensors at different convex surfaces of a spacecraft. Then the estimated heat fluxes can be used to determine the attitude of a spacecraft. To provide this approach, it is essential to consider two inverse problems of heat transfer. Thus, the authors aim to solve these problems, which are challenging. This paper is dedicated to the solution of the second inverse problem. It was shown that one can obtain sufficiently accurate results on the basis of a constrained set of relatively simple temperature measurements.

Estimation of transient boundary heat flux by using hybrid algorithm in a two dimensional laminar duct flow

Conjugate gradient method (CGM) with adjoint problem is a popular optimization algorithm in solving the inverse heat transfer problems. It starts with the initial guess solution of unknown parameters to be estimated which would be updated in an iterative procedure. The initial guess solution is one of the significant factors for the accuracy of estimation. In the current study, the Jaya algorithm has been developed to provide the initial guess solution to CGM. The resultant algorithm is called hybrid algorithm. The test problem considered here for the study is the estimation of transient boundary heat flux for two-dimensional hydrodynamically developed and thermally developing forced convective laminar duct flow. The hybrid algorithm is found to be robust and accurate than CGM.