On the Heat Transfer Enhancement of Turbulent Gas Floes in Short Round Tubes Engaging a Light Gas Mixed With Selected Heavier Gases

Abstract

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 as the principal gas and xenon, nitrogen, oxygen, carbon dioxide, methane, tetrafluoromethane and sulfur hexafluoride 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 ηmix, thermal conductivity λmix, density ρmix, and heat capacity at constant pressure. The quartet ηmix, λmix, ρmix, and Cp,mix is represented by triple-valued functions of the film temperature the pressure P, and the molar gas composition w. The viscosity is obtained from the Kinetic Theory of Gases conjoined with the Chapman-Enskog solution of the Boltzmann Transport Equation. The thermal conductivity is computed from the Kinetic Theory of Gases. The density is determined with a truncated virial equation of state. The heat capacity at constant pressure 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 five binary gas mixtures He-Xe, He-N2, He-O2, He-CO2, He-CH4, He-CF4 and He-SF6 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 hmix/B versus the molar gas composition w is graphed in congruous diagrams. At a low film temperature Tf = 300 K, the global maximum allied mean convection coefficient hmix,max/B = 85 is furnished by the He-SF6 gas mixture at an optimal molar gas composition wopt = 0.93. The global maximum allied mean convection coefficient hmix,max/B = 57 is supplied by pure methane gas SF6 (w = 1) at a high film temperature Tf = 1000 K instead of the He-SF6 gas mixture.