Details
| Original language | English |
|---|---|
| Pages (from-to) | 768-782 |
| Number of pages | 15 |
| Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |
| Volume | 90 |
| Issue number | 10-11 |
| Publication status | Published - 16 Jul 2010 |
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
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Mathematics(all)
- Applied Mathematics
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In: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 90, No. 10-11, 16.07.2010, p. 768-782.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A micromechanically motivated higher-order continuum formulation of linear thermal conduction
AU - Temizer, I.
AU - Wriggers, P.
PY - 2010/7/16
Y1 - 2010/7/16
N2 - 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.
AB - 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.
KW - Burnett equations.
KW - Higher-order continuum
KW - Size effects
KW - Thermal conduction
UR - http://www.scopus.com/inward/record.url?scp=78349302603&partnerID=8YFLogxK
U2 - 10.1002/zamm.201000009
DO - 10.1002/zamm.201000009
M3 - Article
AN - SCOPUS:78349302603
VL - 90
SP - 768
EP - 782
JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
SN - 0044-2267
IS - 10-11
ER -