Connections Between Stability, Convexity of Internal Energy, and the Second Law for Compressible Newtonian Fluids

Bechtel, Stephen E.; Rooney, Frank; Forest, M. Gregory

doi:10.1115/1.1831297

Cited by 36 publications

(17 citation statements)

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“…In this section, we look into the conditions required for such a stable equilibrium state. A consequence of this requirement is that the internal energy of the material must be a convex function of the extensive variables, which is imposed as follows [6]:…”

Section: Thermodynamic Stabilitymentioning

confidence: 99%

Thermodynamic restrictions on linear reversible and irreversible thermo-electro-magneto-mechanical processes

Santapuri

2016

Heliyon

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A unified thermodynamic framework for the characterization of functional materials is developed. This framework encompasses linear reversible and irreversible processes with thermal, electrical, magnetic, and/or mechanical effects coupled. The comprehensive framework combines the principles of classical equilibrium and non-equilibrium thermodynamics with electrodynamics of continua in the infinitesimal strain regime.In the first part of this paper, linear Thermo-Electro-Magneto-Mechanical (TEMM) quasistatic processes are characterized. Thermodynamic stability conditions are further imposed on the linear constitutive model and restrictions on the corresponding material constants are derived. The framework is then extended to irreversible transport phenomena including thermoelectric, thermomagnetic and the state-of-the-art spintronic and spin caloritronic effects. Using Onsager's reciprocity relationships and the dissipation inequality, restrictions on the kinetic coefficients corresponding to charge, heat and spin transport processes are derived. All the constitutive models are accompanied by multiphysics interaction diagrams that highlight the various processes that can be characterized using this framework.

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Section: Thermodynamic Stabilitymentioning

confidence: 99%

Thermodynamic restrictions on linear reversible and irreversible thermo-electro-magneto-mechanical processes

Santapuri

2016

Heliyon

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“…The subsequent analysis leans essentially on thermodynamic stability of the fluid system expressed through The above relations reflect stability of the equilibrium solutions to the Navier-Stokes-Fourier system (see Bechtel, Rooney, and Forest [1]) and play a crucial role in the study of the long-time behavior of solutions, see [19,Chapters 5,6]. Last but not least, as we will see below, the relations (1.18), (1.19) represent the key ingredient in the proof of weak-strong uniqueness.…”

Section: Constitutive Relationsmentioning

confidence: 99%

Navier--Stokes--Fourier System on Unbounded Domains: Weak Solutions, Relative Entropies, Weak-Strong Uniqueness

Jesslé¹,

Jin²,

Novotný³

2013

SIAM J. Math. Anal.

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We investigate the Navier-Stokes-Fourier system describing the motion of a compressible, viscous and heat conducting fluid on large class of unbounded domains with no slip and slip boundary conditions. We propose a definition of weak solutions, that is particularly convenient for the treatment of the Navier-Stokes-Fourier system on unbounded domains. We prove existence of weak solutions for arbitrary large initial data for potential forces with an arbitrary growth at large distances. We show, that any weak solution satisfies the so called relative entropy inequality. Finally we prove the weak-strong uniqueness principle, meaning that the weak solutions coincide with strong solutions emanating from the same initial data (as long as the latter exist), at least when the potential force vanishes at large distances.

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“…Bechtel, Rooney and Forest [11]. The former condition in (2.5) says that compressibility of the fluid is always positive, while the latter means that specific heat at constant volume is positive.…”

Section: Thermodynamic Stability Equilibrium Statesmentioning

confidence: 99%

Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems

Feireisl

2010

Milan J. Math.

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Connections Between Stability, Convexity of Internal Energy, and the Second Law for Compressible Newtonian Fluids

Cited by 36 publications

References 1 publication

Thermodynamic restrictions on linear reversible and irreversible thermo-electro-magneto-mechanical processes

Thermodynamic restrictions on linear reversible and irreversible thermo-electro-magneto-mechanical processes

Navier--Stokes--Fourier System on Unbounded Domains: Weak Solutions, Relative Entropies, Weak-Strong Uniqueness

Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems

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