A micromechanically motivated higher-order continuum formulation of linear thermal conduction

verfasst von: I. Temizer, P. Wriggers
Abstract: A higher-order continuum theory of linearized thermal conduction is developed where a rigid heat conductor is modeled as a material of grade-2 with a view towards capturing the thermal effects in BGK-Burnett type formulations for microfluidic flows. The construction is based on a second-order thermal homogenization framework which leads to the identification of a thermal dissipation potential that is a function of the higher-order gradients of the temperature. The dissipation potential delivers the expressions for the higher-order fluxes and forms the basis of a discussion regarding the satisfaction of the second law of thermodynamics. Further restrictions on the constitutive expressions arise from material symmetry considerations. Strong and weak formulations of the associated boundary value problem are derived based on an appropriate identification of the boundary conditions. The methodologies employed and the implications of the theory are reminiscent of similar approaches in linearized elasticity formulations and are compared with micromorphic and Cahn-Hilliard type formulations.A higher-order continuum theory of linearized thermal conduction is developed where a rigid heat conductor is modeled as a material of grade-2 with a view towards capturing the thermal effects in BGK-Burnett type formulations for microfluidic flows. The construction is based on a second-order thermal homogenization framework which leads to the identification of a thermal dissipation potential that is a function of the higher-order gradients of the temperature. The dissipation potential delivers the expressions for the higher-order fluxes and forms the basis of a discussion regarding the satisfaction of the second law of thermodynamics. Further restrictions on the constitutive expressions arise from material symmetry considerations. Strong and weak formulations of the associated boundary value problem are derived based on an appropriate identification of the boundary conditions. The methodologies employed and the implications of the theory are reminiscent of similar approaches in linearized elasticity formulations and are compared with micromorphic and Cahn-Hilliard type formulations.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Typ: Artikel
Journal: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Band: 90
Seiten: 768-782
Anzahl der Seiten: 15
ISSN: 0044-2267
Publikationsdatum: 16.07.2010
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.1002/zamm.201000009 (Zugang: Unbekannt)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{eae6a06bd9e04e06b1a70eb120e69a8f,
title = "A micromechanically motivated higher-order continuum formulation of linear thermal conduction",
abstract = "A higher-order continuum theory of linearized thermal conduction is developed where a rigid heat conductor is modeled as a material of grade-2 with a view towards capturing the thermal effects in BGK-Burnett type formulations for microfluidic flows. The construction is based on a second-order thermal homogenization framework which leads to the identification of a thermal dissipation potential that is a function of the higher-order gradients of the temperature. The dissipation potential delivers the expressions for the higher-order fluxes and forms the basis of a discussion regarding the satisfaction of the second law of thermodynamics. Further restrictions on the constitutive expressions arise from material symmetry considerations. Strong and weak formulations of the associated boundary value problem are derived based on an appropriate identification of the boundary conditions. The methodologies employed and the implications of the theory are reminiscent of similar approaches in linearized elasticity formulations and are compared with micromorphic and Cahn-Hilliard type formulations.A higher-order continuum theory of linearized thermal conduction is developed where a rigid heat conductor is modeled as a material of grade-2 with a view towards capturing the thermal effects in BGK-Burnett type formulations for microfluidic flows. The construction is based on a second-order thermal homogenization framework which leads to the identification of a thermal dissipation potential that is a function of the higher-order gradients of the temperature. The dissipation potential delivers the expressions for the higher-order fluxes and forms the basis of a discussion regarding the satisfaction of the second law of thermodynamics. Further restrictions on the constitutive expressions arise from material symmetry considerations. Strong and weak formulations of the associated boundary value problem are derived based on an appropriate identification of the boundary conditions. The methodologies employed and the implications of the theory are reminiscent of similar approaches in linearized elasticity formulations and are compared with micromorphic and Cahn-Hilliard type formulations.",
keywords = "Burnett equations., Higher-order continuum, Size effects, Thermal conduction",
author = "I. Temizer and P. Wriggers",
year = "2010",
month = jul,
day = "16",
doi = "10.1002/zamm.201000009",
language = "English",
volume = "90",
pages = "768--782",
journal = "ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik",
issn = "0044-2267",
publisher = "Wiley-VCH Verlag",
number = "10-11",
}