%0 Journal Article
%A Campo, Antonio
%A Chikh, Salah
%D 2005
%I Begell House
%N 4
%P 247-265
%R 10.1615/HeatTransRes.v36.i4.10
%T On the Maximization of Turbulent Free Convection along Heated Vertical Plates by Means of Preferable Gaseous Media
%U http://dl.begellhouse.com/journals/46784ef93dddff27,48fce8690b73cc45,1b0ad36240bacc6b.html
%V 36
%X A unique way for maximizing turbulent free convection from heated vertical plates to cold gases is studied in this paper. The central idea 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}), and methane (CH_{4}) as secondary gases may bring forward. From fluid physics, it is known that the thermo-physical 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 Gr_{x} > 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 five binary gas mixtures He-Xe, He-N_{2}, He-O_{2}, He-CO_{2}, and He-CH_{4} 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 five binary gas mixtures utilized, the allied mean convection coefficient *h*_{mix}/*B* versus the molar gas composition w is graphed in congruous diagrams. At a low film temperature *T*_{f} = 300 K, the global maximum allied mean convection coefficient *h*_{mix,max}/*B* = 85 is furnished by the He-Xe gas mixture at an optimal molar gas composition wopt = 0.93. The global maximum allied mean convection coefficient *h*_{mix,max}/*B* = 57 is supplied by pure methane gas CH_{4} (*w* = 1) at a high film temperature *T*_{f} = 1000 K instead of the He-CH_{4} gas mixture.
%8 2005-07-01