An analytical transfer function method to solve inverse heat conduction problems

This work proposes a transfer function identification (or impulse response) method to solve inverse heat conduction problems. The technique is based on Green’s function and the equivalence between thermal and dynamic systems. The inverse heat conduction problems, 1D and 3D transient named X22X22 and X33Y33Z33X33Y33Z33, respectively, 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 the 3D-transient problem studied describes a machining process. From the temperature profile (hypothetical or experimental temperature far from the heat source) and knowing the transfer function it is possible to estimate the heat flux by different approaches: deconvolution, spectral densities estimation or inverse fast Fourier procedure. MATLAB codes were used. The work is concluded with the application of the technique in an experimental case of temperature estimation at the tool-work-piece interface during a machining process.