Publications Repository - Gdańsk University of Technology

The seminal Navier-Stokes equations have been stated yet before creation of principles of thermodynamics and the first and second laws. In the literature there is the common opinion that the Navier-Stokes equations cannot be taken as a thermodynamically correct model of “working fluid” which is able to describe transformation of “ heat” into “work” and vice versa. Therefore, in the paper, a new exposition of thermodynamically consistent Navier-Stokes equations is presented. Keeping the line of reasoning, based on the Gyftopoulos and Beretta concept of thermodynamics [1], we will introduce the basic concepts of thermodynamics with the notion of “heating” and “working” fluxes, and will extend the Gyftopoulos and Beretta approach into three-dimensional continuum thermodynamics. In our approach notion of “energy” and “energy interactions” play a dominant role. The main inconsistencies connected with the internal energy concept as a form of ,,energy storage’’ and the transformations of different forms of energy are evaluated. Thus, the balance of energy is finally presented as a sum of internal, kinetic, potential and radiation energies in the system that are compensated by the total energy flux, which consists of working, heating, chemical, electric, magnetic and radiation energy fluxes at the system boundaries. The law of energy conservation can be considered as the most important one which is superior over any other laws of nature. Summarizing of the consequences of the Gyftopoulos-Beretta thermodynamics exposition – the presented above mathematical model of continuum – the neo-classical Navier-Stokes - has a thermodynamic consistency, what means that unknown fields assigned from a proper set of governing equations must additionally fulfill the condition of not creating energy from nothing [Se= 0 , eq.(9)].

Authors

• dr inż. Paweł Ziółkowski link open in new tab ,
• Janusz Badur