Invariant forms of conservation equations and some examples of their exact solutions

Siavash H Sohrab*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationSymposia
Subtitle of host publicationFundamental 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
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791846230
DOIs
StatePublished - Jan 1 2014
EventASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting, FEDSM 2014, Collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels - Chicago, United States
Duration: Aug 3 2014Aug 7 2014

Publication series

NameAmerican Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM
Volume1C
ISSN (Print)0888-8116

Other

OtherASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting, FEDSM 2014, Collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels
CountryUnited States
CityChicago
Period8/3/148/7/14

Keywords

  • Boundary layer
  • Conservation equations
  • Fluid mechanics
  • Superposition principle in fluid mechanics

ASJC Scopus subject areas

  • Mechanical Engineering

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    Sohrab, S. H. (2014). Invariant forms of conservation equations and some examples of their exact solutions. In 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 (American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM; Vol. 1C). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/FEDSM2014-21154