Thermal characterisation of homogeneous materials using a weak formulation technique

A new method for the thermal characterisation of homogeneous materials is proposed. This method, specifically designed to measure the thermal diffusivity in the plane of thin specimens, is based on a low-order weak formulation (LOWF) method of the heat equation using a virtual test function. In this formulation, the spatial derivatives of temperature are coupled with an analytical expression less dependent on measurement noise. In this way, it is shown that the LOWF method leads to a robust method for the estimation of thermal diffusivity. The LOWF method is numerically tested on a two-dimensional model and validated on a homogeneous material using infrared thermography.