Kinetic theory of piston problem and thermal disturbance by the ellipsoidal statistical model

Abstract

The formation of shock waves by a moving piston and the thermal disturbance of a fixed wall by sudden temperature change are studied according to the kinetic theory of gases. The Ellipsoidal Statistical model which gives the correct Prandtl number for a monatomic gas has been solved numerically. Also, the perturbation method proposed by Chu is also applied. Velocity, density, temperature and pressure distributions have been calculated at each time step for various piston speeds for the piston problem. A comparison between the Bhatnager-Gross-Krook model solution and the Ellipsoidal Statistical model solution has been made. The thermal disturbances of velocity, density and temperature have I also been calculated at each time step for various wall temperatures. A comparison between the Kovitz-Hellman solutions and the Ellipsoidal model has been made.