A remark on the theory of measuring thermal diffusivity by the modified Ångström's method

Abstract

The theory of measuring thermal diffusivity by the modified Ångström's method is extended to the case in which the sample's radiative heat dissipation occurs from its end surface. The formulas deriving the sample's thermal diifusivity from the amplitude decay and phase lag of the temperature wave traveling through the sample are presented for two different sample configurations: one for a flat disk sample for which only the heat dissipation from the sample's end surface is important, and the other for a sample of finite diameter and length for which the heat dissipations from both the sample's side and end surfaces must be considered. For the flat disk sample, measurement at a single angular frequency of the temperature wave provides data necessary for the determination of the sample's thermal diffusivity. For the sample of finite diameter and length, however, measurements of the temperature wave at two discrete angular frequencies are necessary to obtain a complete solution for the thermal diffusivity and other unknown constants. In both cases, to determine the sample's thermal conductivity and the surface conductance of the sample's end surface, the heat capacity per unit volume of the sample must be known. Reanalysis of experimental data on two lunar samples under atmospheric and vacuum conditions shows that for a rectangular parallelepiped, 1 × 1 × 2 cm size, the diffusivity values obtained by the new theories are within 5% of those derived by the conventional theory for a finite bar. Probably, the effect of the sample's geometry will become more distinctive if the samples are more elongated or flatter. The analysis also shows that progressively more refined data are required as the measurement theory becomes more complicated.