Investigation on Thermal Loads in Steady-State Conditions with the Use of the Solution to the Inverse Problem
Magda Joachimiak, Damian Joachimiak, Michał Ciałkowski
Abstract
AbstractThe solution to the Cauchy-type inverse problem in the square domain, illustrating the wall of a heating equipment, is investigated in this article. Some calculation examples simulated the stability of the solution to the inverse problem for an equipment operation with various thermal loads. The problem was regularized by the modified Tikhonov method. Regularization parameter was selected based on the Morozov principle. Influence of the random disturbance of heat flux to the solution of the inverse problem was analyzed. Stable solution to this problem was obtained. The impact of the function singularity locations, corresponding to the locations of the heat source, on temperature distribution on a part of the boundary of the analyzed area was investigated. Presented numerical examples were realized for dimensionless functions, which after rescaling can comply with real values of temperature in components of thermal machines and equipment. Additional informationNotes on contributorsMagda JoachimiakMagda Joachimiak is an assistant professor at the Institute of Thermal Engineering, Poznan University of Technology, Poland. She defended her doctoral thesis in 2014. Her current research is focused on heat transfer during thermo-chemical treatment. She is dealing with solving inverse heat conduction equation and its regularization.Damian JoachimiakDamian Joachimiak is an assistant professor at the Institute of Thermal Engineering, Poznan University of Technology, Poland. He obtained a doctoral degree in 2013. He deals with gas flow and heat flow modeling. He is particularly interested in labyrinth seals, power units and machines as well as in thermo-chemical treatment.Michał CiałkowskiMichał Ciałkowski is a full professor at the Institute of Thermal Engineering, Poznan University of Technology, Poland. He received his doctorate in 1978 in the field of fluid mechanics. He is a scholarship holder of the Alexander von Humboldt Foundation (RWTH Aachen, TU Dresden). He is currently working on inverse problems for the heat conductivity equation.