Simultaneous extrema in the entropy production for steady-state fluid flow in parallel pipes
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Robert K. Niven
Abstract
Steady-state flow of an incompressible fluid in parallel pipes can simultaneously satisfy two contradictory extremum principles in the entropy production, depending on the flow conditions. For a constant total flow rate, the flow can satisfy (i) a pipe network minimum entropy production (MinEP) principle with respect to the flow rates, and (ii) the maximum entropy production (MaxEP) principle of Ziegler and Paltridge with respect to the choice of flow regime. The first principle – different to but allied to that of Prigogine – arises from the stability of the steady state compared to non-steady-state flows; it is proven for isothermal laminar and turbulent flows in parallel pipes with a constant power law exponent, but is otherwise invalid. The second principle appears to be more fundamental, driving the formation of turbulent flow in single and parallel pipes at higher Reynolds numbers. For constant head conditions, the flow can satisfy (i) a modified maximum entropy production (MaxEPMod) principle of Županovíc and co-workers with respect to the flow rates, and (ii) an inversion of the Ziegler–Paltridge MaxEP principle with respect to the flow regime. The interplay between these principles is demonstrated by examples.
© de Gruyter 2010
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Articles in the same Issue
- Guest Editorial – Joint European Thermodynamics Conference 10
- Boltzmann's knock: auto-ignition delay times from Arrhenius theory
- Thermodynamical estimation of the limit potentialities of irreversible binary distillation
- Surface tension and excess molar volumes of trimethyl benzene with tetrahydrofuran, tetra chloromethane and dimethyl sulfoxide
- A new perspective on the form of the first and second laws in rational thermodynamics: Korteweg fluids as an example
- Propagation of temperature waves along core-shell nanowires
- Non-equilibrium Stefan–Boltzmann law
- Gibbs–Bogoliubov variational procedure with the square-well reference system
- Physical foundations of evolutionary theory
- Behavior of entropy in non-classical heat conduction of incompressible media
- The balance of spin from the point of view of mesoscopic continuum physics for liquid crystals
- Simultaneous extrema in the entropy production for steady-state fluid flow in parallel pipes
