On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10126186" target="_blank" >RIV/00216208:11320/12:10126186 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00033-011-0189-1" target="_blank" >http://dx.doi.org/10.1007/s00033-011-0189-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00033-011-0189-1" target="_blank" >10.1007/s00033-011-0189-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework

Popis výsledku v původním jazyce

Starting from a simplified framework of the theory of interacting continua in which the mass balance equations are considered for each constituent but the balance of linear momentum and the balance of energy are considered for the mixture as a whole, weprovide a thermodynamic basis for models that include the Allen-Cahn and Stefan equations as particular cases. We neglect the mass flux due to diffusion associated with the components of the mixture but permit the possibility of mass conversion of the phases. As a consequence of the analysis, we are able to show that the reaction (source) term in the mass balance equation leads to the Laplace operator that appears in the Allen-Cahn model and that this term is not related to a diffusive process. This study is complementary to that by Heida et al. (Zeitschrift fur Angewandte Mathematik und Physik (ZAMP) 63, 145-169, 2012), where we neglected mass conversion of the species but considered mass diffusion effects and derived the constitutive

Název v anglickém jazyce

On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework

Popis výsledku anglicky

Starting from a simplified framework of the theory of interacting continua in which the mass balance equations are considered for each constituent but the balance of linear momentum and the balance of energy are considered for the mixture as a whole, weprovide a thermodynamic basis for models that include the Allen-Cahn and Stefan equations as particular cases. We neglect the mass flux due to diffusion associated with the components of the mixture but permit the possibility of mass conversion of the phases. As a consequence of the analysis, we are able to show that the reaction (source) term in the mass balance equation leads to the Laplace operator that appears in the Allen-Cahn model and that this term is not related to a diffusive process. This study is complementary to that by Heida et al. (Zeitschrift fur Angewandte Mathematik und Physik (ZAMP) 63, 145-169, 2012), where we neglected mass conversion of the species but considered mass diffusion effects and derived the constitutive

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BK - Mechanika tekutin

OECD FORD obor

—

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Zeitschrift für Angewandte Mathematik und Physik

ISSN

0044-2275

e-ISSN

—

Svazek periodika

63

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

17

Strana od-do

759-776

Kód UT WoS článku

000307312800009

EID výsledku v databázi Scopus

—