An Expansion Scheme for the Kirchhoff Theory of Acoustic Damping in Long Tubes Containing Rarefied Gases

An expansion scheme is employed to solve the problem of the propagation of acoustic waves in an infinite cylindrical tube. In the governing equations all the terms of the linearised Navier-Stokes equations are retained and in the boundary conditions are incorporated the corrections due to the wall temperature fluctuation and the slip and temperature jump. The only assumption made is that the Stokes layer thickness is much smaller than the wave length Λ and this provides the expansion parameter. The emphasis is laid on the calculation of attenuation coefficient and explicit results are obtained both for large and small values of the tube radius. The scheme is shown to be valid for λ ≪ R where λ is the mean free path and R is the tube radius.