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On Conservation Equation Combinations and Closure Relations

Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7431, USA
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Entropy 2014, 16(7), 3769-3792; https://doi.org/10.3390/e16073769
Received: 14 May 2014 / Revised: 30 June 2014 / Accepted: 1 July 2014 / Published: 7 July 2014
Fundamental conservation equations for mass, momentum and energy of chemical species can be combined with thermodynamic relations to obtain secondary forms, such as conservation equations for phases, an internal energy balance and a mechanical energy balance. In fact, the forms of secondary equations are infinite and depend on the criteria used in determining which species-based equations to employ and how to combine them. If one uses these secondary forms in developing an entropy inequality to be used in formulating closure relations, care must be employed to ensure that the appropriate equations are used, or problematic results can develop for multispecies systems. We show here that the use of the fundamental forms minimizes the chance of an erroneous formulation in terms of secondary forms and also provides guidance as to which secondary forms should be used if one uses them as a starting point. View Full-Text
Keywords: species conservation equations; mechanical energy; internal energy; entropy inequality species conservation equations; mechanical energy; internal energy; entropy inequality
MDPI and ACS Style

Gray, W.G.; Dye, A.L. On Conservation Equation Combinations and Closure Relations. Entropy 2014, 16, 3769-3792.

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