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Invariant Forms of Conservation Equations and Some Examples of Their Exact Solutions

[+] Author Affiliations
Siavash H. Sohrab

Northwestern University, Evanston, IL

Paper No. FEDSM2014-21154, pp. V01CT15A003; 10 pages
doi:10.1115/FEDSM2014-21154
From:
  • ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels
  • Volume 1C, Symposia: Fundamental Issues and Perspectives in Fluid Mechanics; Industrial and Environmental Applications of Fluid Mechanics; Issues and Perspectives in Automotive Flows; Gas-Solid Flows: Dedicated to the Memory of Professor Clayton T. Crowe; Numerical Methods for Multiphase Flow; Transport Phenomena in Energy Conversion From Clean and Sustainable Resources; Transport Phenomena in Materials Processing and Manufacturing Processes
  • Chicago, Illinois, USA, August 3–7, 2014
  • Conference Sponsors: Fluids Engineering Division
  • ISBN: 978-0-7918-4623-0
  • Copyright © 2014 by ASME

abstract

A scale-invariant model of statistical mechanics is described leading to invariant Boltzmann equation and the corresponding invariant Enskog equation of change. A modified form of Cauchy stress tensor for fluid is presented such that in the limit of vanishing intermolecular spacing all tangential forces vanish in accordance with perceptions of Cauchy and Poisson. The invariant forms of mass, thermal energy, linear momentum, and angular momentum conservation equations derived from invariant Enskog equation of change are described. Also, some exact solution of the conservation equations for the problems of normal shock, flow over a flat plate, and flow within a spherical droplet located at the stagnation point of opposed cylindrically-symmetric gaseous jets are presented.

Copyright © 2014 by ASME

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