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Implications of the Dilute Approximation for the Prediction of Heat and Mass Transfer Rates in Multi-Component Systems

[+] Author Affiliations
Ankan Kumar, Sandip Mazumder

Ohio State University

Paper No. IMECE2006-13113, pp. 1-6; 6 pages
doi:10.1115/IMECE2006-13113
From:
  • ASME 2006 International Mechanical Engineering Congress and Exposition
  • Heat Transfer, Volume 1
  • Chicago, Illinois, USA, November 5 – 10, 2006
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 0-7918-4784-5 | eISBN: 0-7918-3790-4
  • Copyright © 2006 by ASME

abstract

Use of the Fick's law of diffusion is inappropriate in multi-component systems comprised of more than two species since it results in local violation of overall mass conservation. One approach that is often used to circumvent this problem is the dilute approximation, in which the conservation of the diluent is not enforced. It is generally believed that if the mass fraction of the diluent is "large" and it is a non-reacting species, the dilute approximation yields accurate results. In this study, the accuracy of the dilute approximation is quantitatively assessed by comparing its predictions against a rigorous multi-component diffusion formulation, derived from the Stefan-Maxwell equation. Both mass and heat flux errors are computed for a one-dimensional pure diffusion problem. It is found that even for quite dilute mixtures with mass fraction of the diluent exceeding 70%, the errors are ~15% for mass fluxes and as high as 35% for heat fluxes. In addition, the errors are found to be strongly dependent on the type of species in the mixture, implying that the validity of the dilute approximation cannot be judged a priori. Additional results are presented to show that in systems with combined heat and mass diffusion, net heat transfer can occur against the imposed temperature gradient. A Second Law analysis is presented and performed to corroborate these non-intuitive results.

Copyright © 2006 by ASME

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