Estimation of the heat flux imposed by a diode-laser on a paste

In this work, the heat flux imposed by a diode-laser on the surface of a paste sample was estimated by solving an inverse parameter estimation problem. The inverse problem was solved with temperature measurements taken over the heated surface of the sample by an infrared camera. The mathematical model involved heat conduction in the material, by assuming that the diode-laser heat flux was totally absorbed on its surface, which was painted with graphite ink. Based on the qualitative information provided by the temperature measurements, the diode-laser heat flux on the boundary was approximated by a Gaussian function. The parameters of this function, namely the central heat flux and the decay factor, were estimated with classical and Bayesian techniques. The classical techniques included the Levenberg-Marquardt and the conjugate gradient method of minimization of the least squares-norm. The Markov Chain Monte Carlo (MCMC) method implemented via the Metropolis-Hastings algorithm was applied for the solution of the inverse problem within the Bayesian framework of statistics. The sensitivity coefficients were analyzed in this work. While some judged known model parameters, such as the material properties, were deterministically fixed for the application of the classical techniques, their related uncertainties were statistically modeled through the prior distributions for the MCMC method based on independent measured data. The results obtained with the different methods are discussed and compared in the paper, and the residuals between measured and estimated temperatures are analyzed. This work is part of a project for the selection/development of materials for 3D printing of phantoms that can mimic biological tissues, for the study of the thermal treatment of cancer.

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