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The purpose of this work is to formulate a method which can be used to solve nonlinear inverse heat conduction problems and to calculate the heat transfer coefficient distribution on the unknown boundary. The domain under consideration is divided into control volumes in polar coordinates, and heat balance equations are written. Based on temperature transients measured in selected points on the outer surface, temperature values in other points of the domain are determined. Finally, the heat transfer coefficient distribution on the inner surface with the unknown boundary condition is calculated from the presented heat balance equation. The proposed inverse method was verified experimentally using a collector that is part of a semi-industrial laboratory system. This collector is a horizontal, cylindrical thick-walled tank with flat side walls with outlets that enable oil supply and removal. Each side wall has an additional connector to ensure venting. The calculations made it possible to identify the phenomena occurring inside the collector during the experiment. The transient temperature distribution identified by the proposed inverse method was verified by a comparison of the calculated and the measured temperature transients in points inside the collector wall. Very good agreement is observed between the calculated and the measured temperature transients, which confirms the correctness of the identification. This proposed inverse method of the temperature and the heat transfer coefficient calculation is fast enough to apply in online thermal state monitoring systems. The proposed algorithm presented in this paper can easily be implemented industrially.

The presented survey of the up-to-date state of knowledge indicates that despite the great number of works devoted to the issue in question, there is no simple method that allows the use of commercial programs for the identification of the transient thermal state in elements with a simple or complex shape. This paper presents an inverse method developed to estimate the convective heat transfer coefficient varying both in time and space on a vertical plate during its cooling. Despite the smaller number of measurement points and larger disturbance of measured temperatures compared to the data presented in the available literature, comparable results are obtained. The developed iterative algorithm is also applied to estimate the time- and space-dependent heat flux and the convective heat transfer coefficient in the steam boiler membrane waterwall. The analysed component has the form of the non-simply connected and complex shape domain Ω. Temperature-dependent thermophysical properties are used. Calculations are performed for the unknown heat flux or heat transfer coefficient distribution on the domain boundary based on measured temperature transients disturbed with a random error of 0.5 °C. To reduce oscillations, the number of future time steps of NF = 20 is selected. The number of iterations in each time step ranges between 1 and 8. The estimated boundary conditions are close to the exact values. In this work, the ANSYS software using the FEM is applied.

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After a year of the heat exchanger operation in overload conditions, a number of cracks on the tube connections to the tubesheet have been observed. To explain the stress concentration and crack initiation, a finite element analysis is performed. A three-dimensional model is constructed and analyzed. To calculate more precisely the state of stress in the most loaded regions, a submodel is created. The maximum stress exceeds the allowable stress, and according to the standards, it can lead to ratcheting. To reduce stress concentration, all tubes should be shortened and corrugated tubes are installed in the high-temperature region from the side of the burner. A finite element model of the modified heat exchanger and a submodel are created. In the modified heat exchanger, ratcheting should not occur according to the applied standards. During the operation of the modified heat exchanger, there are no further problems with cracking.