Optimally accurate thermal-wave cavity photopyroelectric measurements of pressure-dependent thermophysical properties of air: Theory and experiments

Abstract

An experimental technique for the measurement of thermal properties of air at low pressures using a photopyroelectric (PPE) thermal-wave cavity (TWC) was developed. In addition, two theoretical approaches, a conventional one-dimensional thermal-wave model and a three-dimensional theory based on the Hankel integral, were applied to interpret the thermal-wave field in the thermal-wave cavity. The importance of radiation heat transfer mechanisms in a TWC was also investigated. Radiation components were added to the purely conductive model by linearizing the radiation heat transfer component at the cavity boundary. The experimental results indicate that the three-dimensional model is necessary to describe the PPE signal, especially at low frequencies where thermal diffusion length is large and sideways propagation of the thermal-wave field becomes significant. Radiation is found to be the dominant contributor of the PPE signal at high frequencies and large cavity lengths, where heat conduction across the TWC length is relatively weak. The three-dimensional theory and the Downhill Simplex algorithm were used to fit the experimental data and extract the thermal diffusivity of air and the heat transfer coefficient in a wide range of pressures from 760 to 2.6 Torr. It was shown that judicious adjustments of cavity length and computational best fits to frequency-scanned data using three-dimensional photopyroelectric theory lead to optimally accurate value measurements of thermal diffusivity and heat transfer coefficient at various pressures.