Determination of the Thermal Conductivity Using a Thin-heater Apparatus and a Developed Mathematical Three-layer Model for Edge Heat Losses

Abstract

A thin-heater apparatus based on ASTM C1114 for the determination of the thermal conductivity was designed, built, and tested. The measurement principle holds significant advantages in comparison to the established guarded-hot-plate measurement technique, especially for measurements at very high temperatures. Simulations with finite element method (FEM) show the importance of the consideration of edge heat losses. Thick thermal insulation at the sample sides as well as large sample sizes are traditionally required to reduce the impact of edge heat losses. However, this challenges the need for a robust and efficient measurement system with user-friendly operation and sample handling. It is also often the case that samples of new materials are available only in small sizes. Therefore, ensuing from a one-layer model for the derivation of an edge heat loss correction published by Wolff et al. [1] and Wolff and Guenther [2], a threelayer mathematical model was developed providing a three-dimensional, analytical solution for the exact temperature in a sample stack by using the technique of expanded eigenfunctions. Temperature profiles across the surfaces of both attached heat sinks and a uniform, volumetric Joule heating within a nichrome thin-heater were taken into account. The thermal conductivity of both samples and the heat transfer coefficient defined by Newton’s law of cooling were obtained using a nonlinear fitting method. Finite element analysis (FEA) of the measurement setup is in excellent agreement with the calculation based on the analytical model. Measurements of the NIST standard reference material fumed silica SRM 1459c in the temperature range 50 °C to 450 °C are in close agreement with the NIST reference values. The reported results include the heat transfer coefficient in the specific measurement setup, calculated from measurements of temperatures, electrical heating power, geometries, and the thermal conductivity of the thin-heater material. First measurements of the thermal conductivity of Cotronics 360-5HS thermally insulating material were performed in the temperature range from 60 °C to 915 °C.