*Article* **A Di**ff**erent Approach to Estimate Temperature-Dependent Thermal Properties of Metallic Materials**

#### **Luís Felipe dos Santos Carollo, Ana Lúcia Fernandes de Lima e Silva and Sandro Metrevelle Marcondes de Lima e Silva \***

Heat Transfer Laboratory—LabTC, Institute of Mechanical Engineering—IEM, Federal University of Itajubá—UNIFEI, Campus Prof. José Rodrigues Seabra, Av. BPS, 1303, Itajubá 37500-903, MG, Brazil **\*** Correspondence: metrevel@unifei.edu.br; Tel.: +55-35-3629-1069

Received: 19 July 2019; Accepted: 10 August 2019; Published: 13 August 2019

**Abstract:** Thermal conductivity, λ, and volumetric heat capacity, ρ*cp*, 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 ρ*cp,* and the uncertainty values were above 5%.

**Keywords:** temperature-dependent thermal properties; simultaneous estimation; optimization; sensitivity coefficients; uncertainty analysis
