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This study models plane shock waves in dilute gases using Navier-Stokes-Fourier equations. The soft sphere model accurately fits experimental density profiles, showing viscosity and conductivity depend on temperature.

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Area of Science:

  • Fluid dynamics
  • Thermodynamics
  • Statistical mechanics

Background:

  • Plane shock waves are fundamental phenomena in fluid dynamics.
  • Understanding shock wave structure in dilute gases is crucial for various applications.
  • The Navier-Stokes-Fourier constitutive equations provide a macroscopic framework for fluid behavior.

Purpose of the Study:

  • To investigate plane shock waves in dilute gases using established physical principles.
  • To evaluate the applicability of the soft sphere model in describing shock wave phenomena.
  • To analyze the relationship between gas properties (viscosity, thermal conductivity) and temperature within shock waves.

Main Methods:

  • Utilizing the Navier-Stokes-Fourier constitutive equations for theoretical analysis.
  • Employing the soft sphere model to represent gas molecular interactions.
  • Comparing theoretical predictions with experimental data for normalized density profiles.

Main Results:

  • The Navier-Stokes-Fourier equations were successfully applied to model plane shock waves.
  • The soft sphere model demonstrated a good fit with experimental normalized density profiles.
  • Viscosity and thermal conductivity were found to be proportional to a power of temperature.

Conclusions:

  • The soft sphere model is a suitable approach for describing shock waves in dilute gases.
  • The temperature dependence of viscosity and thermal conductivity is a key factor in shock wave structure.
  • This research validates macroscopic equations for microscale phenomena.