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Onsager's-principle-consistent 13-moment transport equations.

Narendra Singh1, Amit Agrawal1

  • 1Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.

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|July 15, 2016
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Summary
This summary is machine-generated.

This study introduces new transport equations for higher-order moments, improving descriptions of gas flows beyond equilibrium. These generalized equations offer a larger Knudsen number range and fewer boundary conditions than previous models.

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Area of Science:

  • Fluid dynamics
  • Kinetic theory
  • Statistical mechanics

Background:

  • Existing models like Grad's 13-moment equations have limitations in describing non-equilibrium gas flows.
  • The need for accurate transport equations that capture strong deviations from equilibrium is critical in rarefied gas dynamics.

Purpose of the Study:

  • To derive generalized transport equations for higher-order moments.
  • To develop a closure satisfying Onsager's symmetry principle.
  • To provide a more accurate description of gas flows, particularly in the transition regime.

Main Methods:

  • Derivation of generalized transport equations for stress tensor and heat flux.
  • Utilizing a distribution function that satisfies collision invariance and the H-theorem.
  • Comparison with Grad's 13-moments equations for Maxwellian molecules.

Main Results:

  • The proposed equations include higher-order terms than Grad's and R13 equations.
  • The new closure satisfies Onsager's symmetry principle.
  • The derived equations correctly predict the Prandtl number for monatomic gases.

Conclusions:

  • The new equations offer a broader Knudsen number envelope for flow description.
  • Fewer boundary conditions are required compared to R13 equations.
  • The approach provides a robust framework for non-equilibrium gas dynamics.