A mathematical method for the analysis of heat capacity and thermal conductivity measurements by the heat pulse technique

Abstract

We present a new mathematical method for the analysis of heat capacity and thermal conductivity measurements by the heat pulse technique for the case of samples of finite length with a one-dimensional heat flow. In these experiments a heat pulse is produced by a heater, and the temperature is measured as a function of time at a different location on the sample. Finite length effects are taken care of in a natural way, and the thermal conductivity is obtained very simply. In addition, this method is capable of separating the heat capacities of the sample, of the heater and of the thermometer, which may be of practical importance for the case of thin samples with a small heat capacity. The mathematical analysis is based on Laplace transform techniques similar to those used for electrical transmission lines. The analysis of the experimental data is performed by calculating several moments of the temperature rise in the thermometer as a function of time. The method is particularly suitable for on-line computer experiments.