Determination of Thermal Conductivity from a Surface Temperature Measurement: Theory for the 3W Method

摘要

In order to measure thermal conductivity of a material, a so-called 3W method is sometimes used. The key theoretical framework for the 3W method is the determination of a steady-state time-harmonic temperature variation of the solid, whose thermal conductivity is to be measured, when the solid is heated by a time-harmonic heat source. Even though there have been a number of papers published on the 3W method, none of them have provided an exact closed form solution for the steady-state time-harmonic temperature variation of the solid in a form which can lead to an exact closed form expression for the temperature variation amplitude and the phase shift. In this paper, an exact closed form solution is developed for a 1D heat conduction problem with a time-harmonic heat flux. This is a mathematical model for a thermal conductivity measurement for a thin film.