Coupled constitutive relations: a second law based higher-order closure for hydrodynamics.

Area of Science:

• Thermodynamics
• Fluid Mechanics
• Non-equilibrium Systems

Background:

• Classical Navier-Stokes-Fourier equations rely on linear, uncoupled thermodynamic relations.
• These classical equations are limited to systems with small Knudsen numbers.
• They fail to predict phenomena in rarefied gas dynamics.

Purpose of the Study:

• To extend the validity of Navier-Stokes-Fourier equations to higher Knudsen numbers.
• To incorporate nonlinear couplings between thermodynamic forces and fluxes.
• To develop a more comprehensive model for rarefied gas dynamics.

Main Methods:

• Incorporation of nonlinear coupling terms into thermodynamic force-flux relations.
• Derivation of a closed system of conservation laws with coupled constitutive relations.
• Development of phenomenological boundary conditions respecting the second law of thermodynamics.

Main Results:

• The derived system accurately describes rarefaction effects like Knudsen paradox and transpiration flows.
• Predicts phenomena such as thermal stress and heat flux without temperature gradients.
• Demonstrates applicability through benchmark fluid mechanics problems.

Conclusions:

• Nonlinear thermodynamic couplings extend the Navier-Stokes-Fourier equations' validity.
• The new model provides a more accurate description of rarefied gas flows.
• Derived boundary conditions are consistent with thermodynamic principles.