Uso da Transformada de Kirchhoff e Funções de Green para solução analítica de problemas inversos não lineares em condução de calor

Abstract

Heat conduction problems can be observed in many aspects. The importance of understan- ding this phenomenon lies in the process improvement and in the materials characterization. However, it is observed that in most of the processes the variation of thermal properties with temperature occurs, this phenomenon is mainly observed in large temperature variations. Therefore, this work proposes the use of the Kirchhoff’s transform and Green’s functions to determine the analytical solution for the nonlinear unsteady heat conduction with nonlinear boundary condictions. The kirchhoff’s transform is used for problem linearization and the solution of linear version is determined using Green’s functions, so the nonlinear solution is reconstruted using the Kirchhoff’s inverse transform. Comparisons with experimental tem- peratures were made and there was a great agreement of the solution obtained in this work. The inverse approach is also proposed, adapting, for the nonlinear version, the techinque: transfer function based on Green’s functions TFBGF, to estimate heat flux, considering a one-dimensional problem, the aplication of the techinque was efficient to estimate two dis- tinct types of heat flux. It is also proposed to develop a techique for conductivity behavior determination varying with temperature. The technique is based on the application of the Kirchhoff’s transform to determine the polynomial coefficients k(T ). Comparisons of estima- ted coefficients using different forms of k(T ) are shown according to the theoretical values.