Convected acoustic wave motion along a capillary duct with an axial temperature gradient

An analytical solution is presented of the problem of isentropic acoustic wave motion in a circular capillary tube in the presence of both mean flow and a background axial temperature gradient. The main application area is the study of the acoustic effects of catalytic converters. The solution makes use of a series expansion and is valid for only low Mach numbers of mean flow and small relative changes in the background temperature: It is shown that, to the order of approximation used, the solution reduces to that of previous work in both the wide-tube limit and in the limit of zero temperature gradient. A temperature gradient of the magnitude relevant to catalytic converters is shown to have a very marked affect upon the wave attenuation. (C) 1997 Academic Press Limited.