Higher Order Chapman–Enskog Expansion for Dilute Hard Spheres

The matrix elements corresponding to the collision term in the Boltzmann equation for dilute hard spheres were calculated with a computer algebra system and the fast Fourier transform, and utilized to solve the 10th-order Chapman–Enskog (CE) expansion for a steady heat-transfer problem. The solution of the CE expansion was examined using the results of the direct simulation Monte Carlo method and was shown to be a good approximation in the region of moderate Knudsen number.