A thermal analysis of a 5 kVA dry-type transformer under linear and non-linear loads conditions is studied in this paper. The main goal here is to calculate the hottest-spot transformer temperature under free convection through the resolution of the heat conduction equation in three dimensions (3D) using COMSOL Multiphysics®. The proposed technique was validated through experimental data obtained in laboratory. The temperature inside the cores was measured under the influence of free convection. The radiation emission was also measured through a thermal camera. The heat transfer coefficient for both conditions was obtained from empirical correlations. The hottest-spot temperatures were determined from the analysis in the commercial software which was used for the numerical simulations of the transformer heating and cooling under some loading conditions. The temperature residuals, that is, the experimental temperature values subtracted by the numerical temperature values, were below 10%. The numerical analysis found that the hottest-spot temperatures in the core reached 20 °C above the transformer insulation limit. The location of the hottest-spot as well as the obtained temperatures can be used to improve more resistant dry-type transformers.
This work presents a technique called Time Traveling Regularization (TTR) applied to an optimization technique in order to solve ill-posed problems. This new methodology does not interfere in the minimization technique process. The Golden Section method together with TTR are applied only to the objective function which will be minimized. It consists of finding an ideal timeline that minimizes an objective function in a defined future time step. In order to apply the proposed methodology, inverse heat conduction problems were studied. Controlled experiments were performed on 5052 aluminum and AISI 304 stainless steel samples to validate the proposed technique. One-dimensional and three-dimensional heat input experiments were carried out for the 5052 aluminum and AISI 304 stainless steel samples, respectively. The Sequential Function Specification Method (SFSM) was also used to be compared with the results of heat flux obtained by TTR. The estimated heat flux presented a good agreement when compared with experimental values and those estimated by SFSM. Moreover, TTR presented lower residuals than the SFSM.
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