The equations for convection heat transfer and drag forces connected to laminar boundary layer flows

The central idea in this paper is to examine the attributes that binary gas mixtures having helium (He) as the principal gas and xenon (Xe), nitrogen (N₂), oxygen (O₂), carbon dioxide (CO₂), methane (CH₄), tetrafluoromethane (CF₄) and sulfur hexafluoride (SF₆) as secondary gases may bring forward. From fluid physics, it is known that the thermophysical properties affecting free convection with binary gas mixtures are viscosity η_mix, thermal conductivity λ_mix, density ρ_mix, and heat capacity at constant pressure C_p,mix. The quartet η_mix, λ_mix, ρ_mix, and C_p,mix is represented by triple-valued functions of the film temperature T_f, the pressure P, and the molar gas composition w. The viscosity η_mix is obtained from the Kinetic Theory of Gases conjoined with the Chapman-Enskog solution of the Boltzmann Transport Equation. The thermal conductivity λ_mix is computed from the Kinetic Theory of Gases. The density ρ_mix is determined with a truncated virial equation of state. The heat capacity at constant pressure C_p,mix is calculated from Statistical Thermodynamics merged with the standard mixing rule. Using the similarity variable method, the descriptive Navier-Stokes and energy equations for turbulent Grashof numbers Grx > 10⁹ are transformed into a system of two nonlinear ordinary differential equations, which is solved by the shooting method and the efficient fourth-order Runge-Kutta-Fehlberg algorithm. The numerical temperature fields T(x, y) for the seven binary gas mixtures He+CO₂, He+CH₄, He+N₂, He+O₂, He+Xe, He+CF₄ and He+SF₆ are channeled through the allied mean convection coefficient h_mix/B varying w- - ith the molar gas composition w in proper w-domain. For the seven binary gas mixtures utilized, the allied mean convection coefficient h_mix/B versus the molar gas composition w is graphed in congruous diagrams.