High-Temperature Thermal Diffusivity Determination Procedure for Solids and Liquids

A new method for measuring the thermal diffusivity of materials at high temperatures is presented. The method is applicable to solids on Earth and liquids in the reduced gravity environment of space. It is especially suited to levitated liquid metals at elevated temperatures, where thermal diffusivity data are not available. The method is applied in two parts, such that lumped analysis is valid in the first part, and Fourier's law of conduction in the second. In both parts, the spherical specimen is assumed to have been heated to a desired temperature and cooled. An inverse conduction problem is then formulated and solved using Laplace transformation techniques. Using this solution, the sample sizes, and experimentally obtained surface temperature history, the thermal diffusivity is determined by minimizing a function that satisfies the heat balance at the surface. Minimization is performed using a modified quasilinearization algorithm. The method is demonstrated using theoretical cooling curves for three materials-nickel, niobium, and palladium (for Nr = 4 and 10)-and is shown to be accurate. Accuracy is very sensitive to error in the temperature data and increases with better curve fits to the temperature data. An error analysis is also performed, and the effect of errors in the various parameters on the evaluated thermal diffusivity is determined. An experimental study for solids on Earth is suggested before development for implementation in space.