Effects of friction and heat conduction on sound propagation in ducts

A theoretical formulation of the propagation of sound in a viscous and heat conducting medium is presented. The problem is reduced to the determination of two scalar potentials related to pressure and entropy fluctuations respectively, and a vector potential related to vorticity fluctuations. The particular case of a two-dimensional duct of constant width is thoroughly investigated in the low, high, and very high frequency ranges. It is shown that three distinct families of modes may propagate along the duct axis, namely, pressure, entropy, and vorticity dominated modes. Perturbation methods are used to study the variations of attenuation rates, phase velocities, and mode shapes, as a function of frequency and duct width.