Funções de Green: soluções analíticas aplicadas a problemas inversos em condução de calor

Abstract

This work presents the developing of analytical solutions based on Green's function to be applied in inverse problems techniques. Special attention is given to the problems that deals to unknown heat ux input such as the heat generation due to the friction in orthogonal machining processes or to the thermal properties measurement using optimization techniques. The great advantage of using Green's function is the ability of obtaining solutions of complex heat conduction problem that involves transient heat source or non homogenous boundary conditions as heat ux input or prescribed temperature varying with time and space. In this work, analytical solutions of one, two and three-dimensional transient heat conduction problems are presented. A practical application of using analytical solution in optimization problem is also presented. Any inverse or optimization technique has a basic and common characteristic: both of them need to solve the direct solution several times. This characteristic is the cause of the large time consumed. In heat conduction problem, the time consumed is, usually, due to the use of numerical solutions of multidimensional models with rened mesh. In this case, if analytical solutions are available the computational time can be reduced drastically. This study presents the development and application of a 3D-transient analytical solution based on Green's function to obtain thermal properties of solids materials.