Investigation on Thermal Loads in Steady-State Conditions with the Use of the Solution to the Inverse Problem. Issue 11 (4th July 2023) - Joachimiak, Magda; Joachimiak, Damian; Ciałkowski, Michał
Abstract: The 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.