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The purpose of this paper is to present a method for monitoring transient thermal stresses. This paper also presents the analysis of thermal stresses of boiler pressure element heating during the start-up in real conditions. The inverse methods are used to determine the wall temperature, whereas the commercial software ANSYS is used to determine the thermal stresses in the pressure component.

The method is based on the solution of the inverse heat conduction problem. Thermal stresses are determined indirectly taking into account the measured temperature values at selected points on the outer wall of a pressure component. First, the transient temperature distribution in the entire pressure element is calculated, and then, thermal stresses are determined by the finite element method. Measured pressure changes are used to determine the stresses resultant from the internal pressure.

The obtained stresses and temperature in the thick-walled pipe are illustrated and compared with experimental data. Satisfactory agreement was found between computational and experimental results.

The method can be used in the monitoring of thermal and mechanical stresses during the boiler’s start-up and shut-down. Because the temperature distribution at each time level is determined, it can be applied as a thermal load during the structural analysis.

To develop an effective and reliable procedure for the calculation of heat fluxes from the measured temperatures in experimental tests of impingement water cooling.

An inverse heat transfer analysis procedure is developed and implemented into a 2D finite element program. In this method, the least‐squares technique, sequential function specification and regularization are used. Simplifications in the sensitivity matrix calculation and iterative procedures are introduced. The triangular and impulse‐like profiles of heat fluxes simulating practical conditions of impingement water cooling are used to investigate the accuracy and stability of the proposed inverse procedure. The developed program is then used to determine the heat flux during impingement water cooling.

A hybrid procedure is developed in which inverse calculations are conducted with a computation window. This procedure may be used as a whole time domain method or become a periodically sequential or real sequential method by adjusting the sequential steps.

Parametric study and application show that the developed method is effective and reliable and that inverse analysis may obtain the heat flux with an acceptable level of accuracy.

The main aim of this paper is to utilize the different forms of functions for the numerical solution of the two‐dimensional (2‐D) inverse heat conduction problem with temperature‐dependent thermo‐physical properties (TDTPs).

The proposed numerical technique is based on the modified elitist genetic algorithm (MEGA) combined with finite different method (FDM) to simultaneously estimate temperature‐dependent thermal conductivity and heat capacity. In this paper, simulated (noisy and filtered) temperatures are used instead of experimental data. The estimated temperatures are obtained from the direct numerical solution (FDM) of the 2‐D conductive model by using an estimate for the unknown TDTPs and MEGA is used to minimize a least squares objective function containing estimated and simulated (noisy and filtered) temperatures.

The accuracy of the MEGA is assessed by comparing the estimated and the pre‐selected TDTPs. The results show that the measurement errors do not considerably affect the accuracy of the estimates. In other words, the proposed method provides a practical and confident prediction in simultaneously estimating the temperature‐dependent heat capacity and thermal conductivity. From the results, it is found that the RMS error between estimated and simulated temperatures is smaller for linear simulation and also we found this form convenient for parameters estimations.

Future approaches should find the optimal design of case study and then apply the proposed method to achieve the best results.

Applications of the results presented in this paper can be of value in practical applications in parameter estimation even with one sensor temperature history.

This paper aims to present the Cauchy problem for the Laplace’s equation for profiles of gas turbine blades with one and three cooling channels. The distribution of heat transfer coefficient and temperature on the outer boundary of the blade are known. On this basis, the temperature on inner surfaces of the blade (the walls of cooling channels) is determined.

Such posed inverse problem was solved using the finite element method in the domain of the discrete Fourier transform (DFT).

Calculations indicate that the regularization in the domain of the DFT enables obtaining a stable solution to the inverse problem. In the example under consideration, problems with reconstruction constant temperature, assumed on the outer boundary of the blade, in the vicinity of the trailing and leading edges occurred.

The application of DFT in connection with regularization is an original achievement presented in this study.

This paper aims to discuss inverse problems that arise in a variety of practical thermal processes and systems. It presents some of the approaches that may be used to obtain results that lie within a small region of uncertainty. Therefore, the non-uniqueness of the solution is reduced so that the final design and boundary conditions may be determined. Optimization methods that may be used to reduce the uncertainty and to select locations for experimental data and for minimizing the error are presented. A few examples of thermal systems are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems.

In most analytical and numerical solutions, the basic equations that describe the process, as well as the relevant and appropriate boundary conditions, are known. The interest lies in obtaining a unique solution that satisfies the equations and boundary conditions. This may be termed as a direct or forward solution. However, there are many problems, particularly in practical systems, where the desired result is known but the conditions needed for achieving it are not known. These are generally known as inverse problems. In manufacturing, for instance, the temperature variation to which a component must be subjected to obtain desired characteristics is prescribed, but the means to achieve this variation are not known. An example of this circumstance is the annealing, tempering or hardening of steel. In such cases, the boundary and initial conditions are not known and must be determined by solving the inverse problem to obtain the desired temperature variation in the component. The solutions, thus, obtained are generally not unique. This is a review paper, which discusses inverse problems that arise in a variety of practical thermal processes and systems. It presents some of the approaches or strategies that may be used to obtain results that lie within a small region of uncertainty. It is important to realize that the solution is not unique, and this non-uniqueness must be reduced so that the final design and boundary conditions may be determined with acceptable accuracy and repeatability. Optimization techniques are often used for minimizing the error. This review presents several methods that may be applied to reduce the uncertainty and to select locations for experimental data for the best results. A few examples of thermal systems are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems. By considering a variety of systems, the paper also shows the importance of solving inverse problems to obtain results that may be used to model and design thermal processes and systems.

The solution of inverse problems, which frequently arise in thermal processes, is discussed. Different strategies to obtain the conditions that lead to the desired result are given. The goal of these approaches is to reduce uncertainty and obtain essentially unique solutions for different circumstances. The error of the method can be checked against known conditions to see if it is acceptable for the given problem. Several examples are given to illustrate the use of these methods.

The basic strategies presented here for solving inverse problems that arise in thermal processes and systems, as well as the optimization techniques used to reduce the domain of uncertainty, are fairly original. They are used for certain challenging problems that have not been considered in detail earlier. Several methods are outlined for considering different types of problems.

The purpose of this paper is to present the method for solving the inverse Cauchy-type problem for the Laplace’s equation. Calculations were made for the rectangular domain with the target temperature on three boundaries and, additionally, on one of the boundaries, the heat flux distribution was selected. The purpose of consideration was to determine the distribution of temperature on a section of the boundary of the investigated domain (boundary Γ₁) and find proper method for the problem regularization.

The solution of the direct and the inverse (Cauchy-type) problems for the Laplace’s equation is presented in the paper. The form of the solution is noted as the linear combination of the Chebyshev polynomials. The collocation method in which collocation points had been determined based on the Chebyshev nodes was applied. To solve the Cauchy problem, the minimum of functional describing differences between the target and the calculated values of temperature and the heat flux on a section of the domain’s boundary was sought. Various types of the inverse problem regularization, based on Tikhonov and Tikhonov–Philips regularizations, were analysed. Regularization parameter α was chosen with the use of the Morozov discrepancy principle.

Calculations were performed for random disturbances to the heat flux density of up to 0.01, 0.02 and 0.05 of the target value. The quality of obtained results was next estimated by means of the norm. Effect of the disturbance to the heat flux density and the type of regularization on the sought temperature distribution on the boundary Γ₁ was investigated. Presented methods of regularization are considerably less sensitive to disturbances to measurement data than to Tikhonov regularization.

Discussed in this paper is an example of solution of the Cauchy problem for the Laplace’s equation in the rectangular domain that can be applied for determination of the temperature distribution on the boundary of the heated element where it is impossible to measure temperature or the measurement is subject to a great error, for instance on the inner wall of the boiler. Authors investigated numerical examples for functions with singularities outside the domain, for which values of gradients change significantly within the calculation domain what corresponds to significant changes in temperature on the wall of the boiler during the fuel combustion.

In this paper, a new method for solving the Cauchy problem for the Laplace’s equation is described. To solve this problem, the Chebyshev polynomials and nodes were used. Various types of regularization of this problem were considered.

Investigates errors of the reconstruction temperatures at boundaries caused by variation of the locations of two temperature sensors in a one‐dimensional inverse heat conduction problem (IHCP) by using a time marching implicit finite difference inverse solver. Numerical simulation results of selected functions indicate that errors of the reconstruction temperature at each boundary can be presented by a simple relation. Each relation contains an unknown coefficient which can be determined by using one numerical simulation through the inverse solver of a pair specified sensor locations. This relation can then be used for estimating the other recovery errors at the boundary without using the inverse solver.

In this paper, the Cauchy-type problem for the Laplace equation was solved in the rectangular domain with the use of the Chebyshev polynomials. The purpose of this paper is to present an optimal choice of the regularization parameter for the inverse problem, which allows determining the stable distribution of temperature on one of the boundaries of the rectangle domain with the required accuracy.

The Cauchy-type problem is ill-posed numerically, therefore, it has been regularized with the use of the modified Tikhonov and Tikhonov–Philips regularization. The influence of the regularization parameter choice on the solution was investigated. To choose the regularization parameter, the Morozov principle, the minimum of energy integral criterion and the L-curve method were applied.

Numerical examples for the function with singularities outside the domain were solved in this paper. The values of results change significantly within the calculation domain. Next, results of the sought temperature distributions, obtained with the use of different methods of choosing the regularization parameter, were compared. Methods of choosing the regularization parameter were evaluated by the norm N_max.

Calculation model described in this paper can be applied to determine temperature distribution on the boundary of the heated wall of, for instance, a boiler or a body of the turbine, that is, everywhere the temperature measurement is impossible to be performed on a part of the boundary.

The paper presents a new method for solving the inverse Cauchy problem with the use of the Chebyshev polynomials. The choice of the regularization parameter was analyzed to obtain a solution with the lowest possible sensitivity to input data disturbances.

The purpose of this paper is to develop a numerical model of a steam pipeline connecting a boiler with a turbine, with an insulated outer surface. The temperature distribution inside the pipeline wall was compared when was perfectly insulated and when used real insulation on the outside surface.

The transient temperature, pressure and velocity of steam in the pipeline were determined using a proposed numerical model with distributed parameters. To calculate the transient temperature of the steam and pipeline wall the finite volume method was used. The energy conservation equations were written for all control area around all the nodes. The heat balance equations are a system of first-order ordinary differential equations with respect to time. The Runge–Kutta method of the fourth-order was used to solve the system of ordinary differential equations of the first-order.

The temperature distribution in the pipeline wall and the temperature distribution in wall insulation were presented. Also, the temperature of the steam and pipeline wall as a function of insulation thickness was calculated. Based on the results obtained by the proposed numerical model, thermal stresses at the inner and outer surface of the component were determined. To assess the accuracy of the proposed model, the results were compared to the analytical solution for the steady state.

The paper presents the results obtained from calculations using a numerical model of the steam pipeline with the actual insulation on the outer surface.