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Entropy 2014, 16(7), 3769-3792; doi:10.3390/e16073769
Article

On Conservation Equation Combinations and Closure Relations

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Received: 14 May 2014; in revised form: 30 June 2014 / Accepted: 1 July 2014 / Published: 7 July 2014
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Abstract: 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

Gray WG, Dye AL. On Conservation Equation Combinations and Closure Relations. Entropy. 2014; 16(7):3769-3792.

Chicago/Turabian Style

Gray, William G.; Dye, Amanda L. 2014. "On Conservation Equation Combinations and Closure Relations." Entropy 16, no. 7: 3769-3792.


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