Exact solutions for shock waves in dilute gases

Area of Science:

• Fluid dynamics
• Gas dynamics
• Non-equilibrium thermodynamics

Background:

• Becker (1922) provided an exact solution for gas shock waves using Navier-Stokes-Fourier equations with constant transport coefficients.
• Subsequent research explored extensions for implicit exact solutions under specific conditions.

Purpose of the Study:

• To investigate exact implicit solutions for shock waves in gases within the soft-spheres model.
• To analyze the impact of temperature-dependent viscosity and thermal conductivity (η, κ ∝ T^σ) on shock wave behavior.

Main Methods:

• Utilized the soft-spheres model where viscosity and thermal conductivity are power functions of temperature.
• Derived and presented implicit exact solutions for specific viscosity indices (σ).

Main Results:

• Obtained implicit exact solutions for shock waves under the soft-spheres model.
• Solutions are provided for the Maxwell model (σ=1), hard spheres (σ=1/2), and cases where σ is a natural number.

Conclusions:

• The study successfully extends Becker's findings to a more general case with temperature-dependent transport properties.
• The derived solutions offer valuable insights into gas dynamics under non-ideal conditions.