Sound propagation in a waveguide with finite thermal conduction at the boundary

Abstract

The modal theory of sound propagation in an acoustic waveguide is extended to include the effect of finite heat conduction at the boundaries. A thermal-impedance equation is derived that controls the conduction of heat from the acoustic medium to the waveguide boundary. The thermal impedance is characterized by a single dimensionless parameter that measures dynamic thermal impedance as it ranges continuously from infinitely conducting to fully insulated boundaries. The boundary-value problem in the waveguide is then solved for rigid, no-slip, and finite conducting boundaries. Perturbations from inviscid mode shapes and axial attenuation rates are calculated for the acoustic mode as well as the modal coefficients of the vorticity and entropy modes as they depend upon the thermal-impedance parameter. It is found that the dependence of the preceding quantities on the thermal-impedance parameter is described for the most part by one continuous function of this parameter.