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 (N
2
), oxygen (O
2
), carbon dioxide (CO
2
), methane (CH
4
), tetrafluoromethane (CF
4
) and sulfur hexafluoride (SF
6
) 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 ŋ
mix
, thermal conductivity λ
mix
, density ρ
mix
, and heat capacity at constant pressure C
p,mix
. The quartet ŋ
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 ŋ
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 > 10
⁹
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+CO
2
, He+CH
4
, He+N
2
, He+O
2
, He+Xe, He+CF
4
and He+SF
6
are channeled through the allied mean convection coefficient hmix/B varying with the molar gas composition w in proper w-domain [0, 1]. 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.