Earl Lynn Tipton
University of Missouri-Columbia,
Nuclear Science and Engineering Institute
Advisors: Sudarshan Loyalka, TushaGhosh
Abstract
The Chapman-Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and also, for gas mixtures, the diffusion coefficient. Due to the very complex nature of the solution expressions, direct, general expressions have been limited to low order solutions (order 3). Studies of high precision computation of the transport coefficients based upon the Chapman-Enskog solutions of the Boltzmann equation have been limited to approaches which require the assumption of the rigid-sphere molecular potential model. We report the results of our investigation of relatively high-order, standard, Sonine polynomial expansions (order 60 +) for the Chapman-Enskog solutions for binary gas mixtures of rigid-sphere molecules for comparative purposes with other computational approaches, which are dependent upon direct numerical techniques. We note that in the current work, we have retained the full dependence of the solution on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals. While in all of the direct numerical methods, more-or-less full calculations need to be carried out with each variation in molecular parameters, our work utilizes explicit, general expressions that retain the complete parametric dependence of the problem. Future application of this work includes exploration of high-order solutions using realistic potential models and the computation of slip and jump coefficients.
Earl Lynn Tipton is a graduate student in the Nuclear Science and Engineering Institute at the University of Missouri-Columbia,
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