Next Article in Journal
Entropy vs. Majorization: What Determines Complexity?
Previous Article in Journal
Maximum Entropy in Drug Discovery
Entropy 2014, 16(7), 3769-3792; doi:10.3390/e16073769

On Conservation Equation Combinations and Closure Relations

*  and
Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7431, USA
* Author to whom correspondence should be addressed.
Received: 14 May 2014 / Revised: 30 June 2014 / Accepted: 1 July 2014 / Published: 7 July 2014
View Full-Text   |   Download PDF [266 KB, uploaded 24 February 2015]


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.
Keywords: species conservation equations; mechanical energy; internal energy; entropy inequality species conservation equations; mechanical energy; internal energy; entropy inequality
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
MDPI and ACS Style

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

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here


[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert