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Thermal conductivity, λ, and volumetric heat capacity, ρcp, variables that depend on temperature were simultaneously estimated in a diverse technique applied to AISI 1045 and AISI 304 samples. Two distinctive intensities of heat flux were imposed to provide a more accurate simultaneous estimation in the same experiment. A constant heat flux was imposed on the upper surface of the sample while the temperature was measured on the opposite insulated surface. The sensitivity coefficients were analyzed to provide the thermal property estimation. The Broydon-Fletcher-Goldfarb-Shanno (BFGS) optimization technique was applied to minimize an objective function. The squared difference objective function of the numerical and experimental temperatures was defined considering the error generated by the contact resistance. The temperature was numerically calculated by using the finite difference method. In addition, the reliability of the results was assured by an uncertainty analysis. Results showing a difference lower than 7% were obtained for λ and ρcp, and the uncertainty values were above 5%.

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.