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.
An adaptive matrix inverse (AMI) method is presented to identify the temperature and unknown boundary heat flux in a domain of a regular or irregular shape with temperature-dependent properties. The nonlinear problem is broken down into a number of linear submodels, and for each submodel, the temperature is obtained in measuring points. Next, based on the matching degree between the temperatures measured and calculated by each prediction submodel, the submodels are weighted and combined to create the full model for the solution of an inverse nonlinear heat transfer problem. Comparisons are also made with the existing multiple model adaptive inverse (MMAI) algorithm and method based on the Levenberg–Marquardt algorithm (LMA). The results of the presented numerical tests for undisturbed and disturbed “measuring” data indicate that the heat fluxes identified by the AMI method are close to the exact values. The application of the presented method for bodies with an irregular shape is also demonstrated. The AMI method has been experimentally verified during the thick-walled cylinder cooling process. The proposed method can be applied in online diagnostic systems for thermal state monitoring.
The paper presents a method of transient temperature estimation in a thick-walled pressure component. Despite the unknown boundary condition on the internal surface of the component, the method allows to determine the temperature distribution thanks to "measured" temperature histories determined in easily accessible points located on the component outer surface. On the outer component surface, heat exchange by radiation and convection is assumed. The proposed method is verified numerically. The presented method for controlling temperature is also suitable for nuclear power plants because it does not require drilling holes for sensors in the pressure element walls.
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.
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