Determinação da difusividade térmica de sólidos através do método do problema inverso

Abstract

Thermal diffusivity of materials is a necessary data for solving problems in different areas, such as food, construction, mechanics, among others. There are different methods of obtaining this data, chosen according to the type of physical system, practicality, accuracy and costeffectiveness. The present work aims to determine the thermal diffusivity of metal samples using the Inverse Problem Method (IP). The Direct Problem (DP) of conduction heat transfer in a bar, with first kind boundary conditions, was numerically solved using the Finite Differences Method. Discretisations of the space and time variables were implemented with the Explicit, Implicit and Crank-Nicolson schemes in order to evaluate their computational performances, aiming at their use in the IP. This was implemented with the Network Search Method, using experimental time temperature data, obtained through an Electronic Data Acquisition System (EDAS). The experiments were performed at the Laboratory of Mathematical Education of UFFS / Chapecó (MEL) and the computer programs were elaborated in Scilab language. The thermal diffusivity of the researched metal was 4,1𝑥10−6 𝑚2/𝑠 obtained by IP and is in the same order of magnitude of steels available in the literature. Such approximation does not confirm the accuracy of the method used, since the steels referred to in the literature probably do not have the same composition as the samples analyzed. However, it can be said that IP is a method: practical because it involves simple and fast experiments; cost-effective because it provides a result in the same order of magnitude as literature data and demands only low-cost electronic materials and the computational execution of a mathematical model.