Função de transferência analítica aplicada à solução de problema inverso em condução de calor

Abstract

This work proposes a heat transfer function identication (or impulse response) method to solve an inverse heat conduction problem. The technique is based on Green\'s function and on a thermal dynamical system equivalent. The inverse heat conduction problems, 1D and 3D transient, respectively, named X22 and X33Y33Z33 are selected to present the fundamentals of the method proposed. The 1D-transient case is a classic heat conduction problem used to obtain thermophysical properties and 3D-transient problem studied describes theoretically a machining process. It is shown that from the temperature prole (hypothetical or experimental temperature measured far from the heat source) and knowing the heat transfer function it is possible to estimate the heat ux by dierent approaches as deconvolution, spectral densities estimation or fast Fourier inverse procedure. MATLAB codes are used. The technique performance for several conguration parameters is presented. For example, parameters as dierent kinds of material (metal or non-metal), geometrical dimensions, sample time and dierent prole of the heat ux are analyzed. The work is concluded with the application of the technique in two experimental cases: i) the heat ux and temperature estimation at the interface of workpiecetool during a machining process and: ii) the heat ux estimation from thermophyscal properties experimental data tests.