Analytical Solutions of Several Ideal Quantum Gas Effusion Flow Problems
Date Issued
2009
Date
2009
Author(s)
Tsai, Ping-Hsue
Abstract
This paper concentrates on several collisionless quantum gas flow problems . The problems concern collisionless flow expanding into vacuum. From a relationship between particle position and velocity, we obtain the corresponding exact solutions for the number density and velocity distributions for the problems. We obtain the exact solutions with 3 distribution functions, which are Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann distribution function, which represent 3 kinds of particles, fermions, bosons and classical particles. Solutions obtained from quantum distribution functions show the differences with classical particles, the quantum effects are found by changing the fugacity of the quantum distribution. In the classical limit, the fugacity is less than 1, three distribution functions converge in the limit. In general the classical particles behave between two quantum particles. Numerical solution results obtained with the direct simulation Monte Carlo method in agreement with the analytical solutions. In general the comparisons between the exact solution and the numerical solutions are virtually identical.
Subjects
Free molecular flow
collisionless flow
quantum effect
ideal quantum gas
analytical solutions
DSMC
Type
thesis
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