Exact Solution for the Thermal Capacitance (Slug) Calorimeter Method

Abstract

The slug calorimeter method can be used for the evaluation of apparent thermal conductivity of fire resistive and other materials at temperatures up to ~1100K [1,2]. Setup consists of a stainless steel plate (slug) of known specific heat, “sandwiched†between two identical flat samples. If the temperature of the samples’ outer surfaces is changing at a constant rate, then the ratio of the slug’s temperature rate to the difference between the samples surfaces’ temperatures eventually becomes proportional to the samples’ thermal conductivity. A more accurate approximate formula and new procedure to get also thermal diffusivity were presented earlier [3]. Now an exact solution of this thermal problem was obtained by applying Duhamel’s convolution integral to the analytical solution for the same setup with constant temperature on its outer surfaces. New accurate formulas were derived and a procedure is proposed for the simultaneous measurements of both thermal diffusivity and volumetric specific heat. Thermal conductivity and thermal effusivity can be calculated too. Validity of the new formulas was verified by numerical experiment using Finite Elements Analysis.