Experimental inverse analysis for the determination of boundary conditions in the parallel hot wire technique

The parallel hot wire technique is considered as an effective and accurate mean of experimental measurement of thermal conductivity. However, the assumptions of infinite medium and ideal, infinitely thin and long heat source, lead to some restrictions in the applicability of this technique. In order to make an effective experiment design, a numerical analysis should be, a priori, carried out which requires a precise specification of the heating source strength and the heat transfer coefficient on the external surface. In this work, a more accurate physical and mathematical modeling of an experimental set-up based on the parallel hot wire method is considered in order to estimate the two above-mentioned parameters from noisy temperature histories measured inside the material. Based on a sensitivity analysis, the heating source strength is estimated first using early time measurements. With such estimated value, determination of the heat transfer coefficient using temperatures measured at later times is then considered. The Levenberg–Marquardt (LM) method is successfully applied using a single experiment for the inverse solution of the two present parameter estimation problems. Estimates of this gradient based deterministic method are validated with a stochastic method (Kalman filter). The effects of the measurement location, the heating duration, the measurement time step and the LM parameter on the estimates and their associated confidence bounds are investigated. Used in the traditional fitting procedure of the parallel hot wire technique, the estimated heating source power provides a reasonable agreement between fitted and exact values of the thermal conductivity and the thermal diffusivity. Determination of the heat transfer coefficient as a function of temperature is also considered.