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 (CO ₂), methane (CH₄), tetrafluoromethane or carbon tetrafluoride (CF₄) and sulfur hexafluoride (SF₆). The three thermophysical properties forming the Prandtl number of binary gas mixtures Pr_mix are heat capacity at constant pressure C _p,mix (thermodynamic property), viscosity η_mix (transport property) and thermal conductivity λ_mix (transport property), which in general depend on temperature T and molar gas composition w. The precise formulas for the calculation of the trio C_p,mix, η_mix, and λ_mix are gathered from various dependable sources. When the set of computed Pr_mix 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 Pr_mix(w) curves exhibited distinctive concave shapes. In the curves format, all Pr _mix(w) curves initiate with Pr ≈ 0.7 at w = 0 (associated with light primary He). Forthwith, each Pr_mix(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 Pr_mix,min = 0.12 at the optimal molar gas composition w_opt = 0.975.