HOT-DISC METHOD APPLIED TO AN INSULATION COATED WITH A THIN, HIGHLY CONDUCTIVE LAYER. MATHEMATICAL REPORT

Report, 2012

The paper “Transient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials” by Silas E. Gustafsson, 1991, presents the following method to measure thermal conductivity. A small, thin circular disc is placed in the center between two slabs of the studied material. The disc is heated electrically. The mean temperature over the disc area is measured as function of time. The thermal conductivity and thermal diffusivity is determined by fitting an analytical solution to the measured temperature curve. The analytical solution for a constant heat source in a circular thin plate imbedded in an infinite surrounding volume of the material is presented by Gustafsson in the paper and preceding publications in the reference list of the paper. In the first part of this study, this analytical solution is derived in a different way that gives somewhat more concise formulas, which require less computer time. The hot-disc method has been used by P. Johansson et al. to determine the thermal conductivity of vacuum insulation panels. A complication is that the panel is coved by a layer of aluminum coating. The coating is quite thin but the thermal conductivity of the coating is up to 1000 times larger than that of the vacuum insulation panel. The heat flow along the coating cannot be neglected. The second part of this study deals with this more complicated transient thermal problem. An analytical solution in the more complicated case is presented in full detail. An explicit formula for the Laplace transform is derived. The solution in the time domain is obtained from an inversion integral in the complex plane. The two solutions are studied in detail in six appended