Derivation of equations for continuum mechanics and thermodynamics of fluids

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10389591" target="_blank" >RIV/00216208:11320/18:10389591 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/referencework/10.1007/978-3-319-13344-7" target="_blank" >https://link.springer.com/referencework/10.1007/978-3-319-13344-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-13344-7_1" target="_blank" >10.1007/978-3-319-13344-7_1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Derivation of equations for continuum mechanics and thermodynamics of fluids

Popis výsledku v původním jazyce

The chapter starts with overview of the derivation of the balance equations for mass, momentum, angular momentum, and total energy, which is followed by a detailed discussion of the concept of entropy and entropy production. While the balance laws are universal for any continuous medium, the particular behavior of the material of interest must be described by an extra set of material-specific equations. These equations relating, for example, the Cauchy stress tensor and the kinematical quantities are called the constitutive relations. The core part of the chapter is devoted to the presentation of a modern thermodynamically based phenomenological theory of constitutive relations. The key feature of the theory is that the constitutive relations stem from the choice of two scalar quantities, the internal energy and the entropy production. This is tantamount to the proposition that the material behavior is fully characterized by the way it stores the energy and produces the entropy. The general theory is documented by several examples of increasing complexity. It is shown how to derive the constitutive relations for compressible and incompressible viscous heat-conducting fluids (Navier-Stokes-Fourier fluid), Korteweg fluids, and compressible and incompressible heat-conducting viscoelastic fluids (Oldroyd-B and Maxwell fluid).

Název v anglickém jazyce

Derivation of equations for continuum mechanics and thermodynamics of fluids

Popis výsledku anglicky

The chapter starts with overview of the derivation of the balance equations for mass, momentum, angular momentum, and total energy, which is followed by a detailed discussion of the concept of entropy and entropy production. While the balance laws are universal for any continuous medium, the particular behavior of the material of interest must be described by an extra set of material-specific equations. These equations relating, for example, the Cauchy stress tensor and the kinematical quantities are called the constitutive relations. The core part of the chapter is devoted to the presentation of a modern thermodynamically based phenomenological theory of constitutive relations. The key feature of the theory is that the constitutive relations stem from the choice of two scalar quantities, the internal energy and the entropy production. This is tantamount to the proposition that the material behavior is fully characterized by the way it stores the energy and produces the entropy. The general theory is documented by several examples of increasing complexity. It is shown how to derive the constitutive relations for compressible and incompressible viscous heat-conducting fluids (Navier-Stokes-Fourier fluid), Korteweg fluids, and compressible and incompressible heat-conducting viscoelastic fluids (Oldroyd-B and Maxwell fluid).

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

ISBN

978-3-319-13344-7

Počet stran výsledku

70

Strana od-do

3-72

Počet stran knihy

3030

Název nakladatele

Springer

Místo vydání

Neuveden

Kód UT WoS kapitoly

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