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Boundary layer variational principles: a case study
Miroslav Grmela1, Iliya V Karlin, Vladimir B Zmievski
1Ecole Polytechnique de Montreal, H3C 3A7 Montréal, Québec, Canada.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
Researchers found a crossover in entropy production minima within boundary layers using Grad's moment equations. This leads to new variational principles for solving boundary conditions in nonequilibrium thermodynamics.
Area of Science:
- Thermodynamics
- Fluid Dynamics
- Mathematical Physics
Background:
- Heat conduction problems are fundamental in various scientific disciplines.
- Grad's moment equations provide a framework for analyzing rarefied gas dynamics and transport phenomena.
- Understanding entropy production is crucial for characterizing irreversible processes.
Purpose of the Study:
- To investigate the structure of entropy production minima in boundary layers under Grad's moment equations.
- To develop and compare variational principles for addressing boundary conditions in nonequilibrium thermodynamics.
Main Methods:
- Modeling the heat conduction problem using Grad's moment equations.
- Analyzing the behavior of entropy production within the boundary layer.
- Formulating and comparing variational principles.
Main Results:
- A crossover in the structure of entropy production minima was identified within the boundary layer.
- The study demonstrates the applicability of the observed crossover for formulating variational principles.
Conclusions:
- The findings offer new insights into the behavior of entropy production in boundary layers.
- The developed variational principles provide a novel approach to solving boundary value problems in nonequilibrium thermodynamics.