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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.v36.i4.10
pages 247-265

On the Maximization of Turbulent Free Convection along Heated Vertical Plates by Means of Preferable Gaseous Media

Antonio Campo
Department of Mechanical Engineering, The University of Vermont, Burlington, VT 05405, USA
Salah Chikh
USTHB, Faculty of Mechanical and Process Engineering, LTPMP, Alger 16111, Algeria

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 (He) as the principal gas and xenon (Xe), nitrogen (N2), oxygen (O2), carbon dioxide (CO2), and methane (CH4) 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 Cp,mix. The quartet ηmix, λmix, ρmix, and Cp,mix is represented by triple-valued functions of the film temperature Tf, the pressure P, and the molar gas composition w. The viscosity ηmix is obtained from the Kinetic Theory of Gases conjoined with the Chapman-Enskog solution of the Boltzmann Transport Equation. The thermal conductivity λmix is computed from the Kinetic Theory of Gases. The density ρmix is determined with a truncated virial equation of state. The heat capacity at constant pressure Cp,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 five binary gas mixtures He-Xe, He-N2, He-O2, He-CO2, and He-CH4 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 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-Xe 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 CH4 (w = 1) at a high film temperature Tf = 1000 K instead of the He-CH4 gas mixture.


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