Optimal Molar Gas Composition of Selected Gas Mixtures With Helium that Maximize Turbulent Free Convection Along Vertical Plates

With the goal of intensifying turbulent free convection from heated vertical plates to cold gases, five binary gas mixtures are examined in this technical note. Helium (He) is chosen as the principal gas while xenon (Xe), nitrogen $(N2)$⁠, oxygen $(O2)$⁠, carbon dioxide $(CO2)$⁠, and methane $(CH4)$ are the companion gases. From thermal physics, the thermophysical properties affecting turbulent free convection of binary gas mixtures are the viscosity $μmix$⁠, the thermal conductivity $λmix$⁠, the density $ρmix$⁠, and the heat capacity at constant pressure $Cp,mix$⁠. Invoking the similarity variable transformation, the system of two nonlinear differential equations is solved numerically by the shooting method and a fourth-order Runge-Kutta-Fehlberg algorithm. From the numerical temperature fields, the allied mean convection coefficients $h¯mix∕B$ changing with the molar gas composition $w$ in the $w$ domain [0, 1] are plotted in congruous diagrams for the five binary gas mixtures under study.