Improvement and comparison of some estimators dedicated to thermal diffusivity estimation of orthotropic materials with the 3D-flash method

Abstract

This theoretical and numerical study deals with the estimation of thermal diffusivities of orthotropic materials with the 3D-laser-flash method. This method consists in applying a short non-uniform heat flux to a sample in order to generate three-dimensional heat transfer. An infrared camera is used to measure the evolution of the temperature field at the front face or at the back face of the sample. An estimation procedure, i.e., an estimator, combines these measurements with an analytical solution of the underlying model in order to estimate unknown parameters, i.e., thermal diffusivities, a heat transfer coefficient and parameters related to the spatial shape of the laser beam. In this work, three estimators inspired from previous work are presented and some improvements are proposed. A fourth estimator is introduced and compared to the previous ones. This comparison is based on theoretical standard deviations of thermal diffusivities. Results show that standard deviations can vary up to a factor of 4 and are minimized by using the fourth procedure.