Entropy Analysis of Implicit Heat Fluxes in Multi-Temperature Mixtures.

Area of Science:

• Thermodynamics
• Fluid Mechanics
• Continuum Mechanics

Background:

• Classical mixture theory often uses explicit constitutive relations for stress tensors and interaction forces.
• Two-temperature fluid mixtures require specialized constitutive relations for heat fluxes.
• Frame-indifference is a key principle in developing constitutive equations.

Purpose of the Study:

• To propose novel implicit constitutive relations for heat fluxes in two-temperature fluid mixtures.
• To investigate the constraints imposed by the Second Law of Thermodynamics on these implicit relations.
• To compare the entropy production from explicit and implicit constitutive terms.

Main Methods:

• Development of frame-indifferent implicit constitutive relations for heat fluxes.
• Application of the Second Law of Thermodynamics to derive constraints.
• Analysis of entropy production in both explicit and implicit formulations.

Main Results:

• New implicit constitutive relations for heat fluxes in two-temperature fluid mixtures are established.
• The Second Law of Thermodynamics dictates specific constraints on the implicit terms.
• The magnitude of explicit entropy production is found to be equal to or greater than implicit entropy production.

Conclusions:

• The proposed implicit constitutive relations offer a new framework for analyzing heat transfer in complex fluid mixtures.
• Thermodynamic constraints are crucial for ensuring the physical validity of constitutive models.
• The findings provide a basis for further research into non-equilibrium thermodynamics of fluid mixtures.