Estimation of the minimum Prandtl number for binary gas mixtures formed with light helium and certain heavier gases: Application to thermoacoustic refrigerators

This paper addresses a detailed procedure for the accurate estimation of low Prandtl numbers of selected binary gas mixtures. In this context, helium (He) is the light primary gas and the heavier secondary gases are nitrogen (N2), oxygen (O2), xenon (Xe), carbon dioxide (CO2), methane (CH4), tetrafluoromethane or carbon tetrafluoride (CF4) and sulfur hexafluoride (SF6). The three thermophysical properties forming the Prandtl number of binary gas mixtures Prmix are heat capacity at constant pressure Cp,mix (thermodynamic property), viscosity ηmix (transport property) and thermal conductivity λmix (transport property), which in general depend on temperature T and molar gas composition w. The precise formulas for the calculation of the trio Cp,mix, ηmix, and λmix are gathered from various dependable sources. When the set of computed Prmix values for the seven binary gas mixtures He + N2, He + O2, He + Xe, He + CO2, He + CH4, He + CF4, He + SF6 at atmospheric conditions T = 300 K, p = 1 atm is plotted against the molar gas composition w on the w-domain [0,1], the family of Prmix(w) curves exhibited distinctive concave shapes. In the curves format, all Prmix(w) curves initiate with Pr ≈ 0.7 at w = 0 (associated with light primary He). Forthwith, each Prmix(w) curve descends to a unique minimum and thereafter ascend back to Pr ≈ 0.7 at the terminal point w = 1 (connected to heavier secondary gases). Overall, it was found that among the seven binary gas mixtures tested, the He + Xe gas mixture delivered the absolute minimum Prandtl number Prmix,min = 0.12 at the optimal molar gas composition wopt = 0.975.