Thermal Transport Properties of Layered Materials: Identification by a New Numerical Algorithm for Transient Measurements

摘要

Transient methods are widely used to determine thermal transport properties. In some situations they can be used for homogeneous media to measure several properties either simultaneously or separately. In this context an analytic model is available and a well-posed inverse problem of parameter identification has to be solved. The examination of composite media is more complicated. The algorithm proposed here allows simultaneous determination of the thermal conductivity and thermal diffusivity of layered dielectrics by transient measurements. It is based on a plane source that acts both as a resistive heater and temperature sensor. For the technique to be successful two essential aspects have to be considered: firstly, the mathematical modeling of the measured data (the forward problem) and secondly, the problem of ill-posedness of the inverse problem. For the proposed measurement configuration, a new fast data analysis algorithm based on an analytic solution for the forward problem is presented. In principle, a numerical solution such as an FEM solution of the heat conduction equation can be used instead of the analytical one, but the computational effort is much greater. The inverse problem is formulated as an output-least-squares problem, which leads to a transcendent algebraic system of equations. The method was successfully tested for different situations.