New thermal analysis of the hot disc method based on explicit analytical developments

In this paper, a new approach of the Hot Disc method is presented based on the explicit calculation of the average temperature of a constant heat source on a semi-infinite medium. The Transient Plane Source (TPS) technique developed in the 90 uses a linear regression between the evolution of temperature of the source and a function. This function needs to perform an integral whose calculation can be complex and slow. Therefore, we propose a new approach based on the explicit analytical expression of the average temperature of the heat source to obtain simultaneously by inverse method, the thermal characteristics of the medium, i.e. the conductivity and diffusivity. Besides, we propose to estimate simultaneously the experimental unknown parameters, namely the correction time due to the sensor and the establishment of micro constriction phenomena and the thermal contact resistance between the sensor and the material to be characterized. This approach also makes explicit, for the first time, the sensitivities of the problem and thus to make a complete and accurate sensitivity analysis based on their analytical expressions. Thus, an uncertainty estimation analysis of the parameter estimation using a stochastic approach is carried out to predict confidence intervals on each parameter as a function of the measurement noise. A Monte Carlo method confirms the obtained results. An optimization of the experimental parameters is then conducted based on the minimization of the confidence interval of the estimated parameters.