Analytical solution of the laminar mean flow wave equation in a lined or unlined two-dimensional rectangular duct

The prediction of the sound attenuation in lined ducts with sheared mean flow has been a topic of research for many years. This involves solving the sheared mean flow wave equation, satisfying the relevant boundary condition. As far as the authors' knowledge goes, this has always been done using numerical techniques. Here, an analytical solution is presented for the wave propagation in two-dimensional rectangular lined ducts with laminar mean flow. The effect of laminar mean flow is studied for both the downstream and the upstream wave propagation. The attenuation values predicted for the laminar mean flow case are compared with those for the case of uniform mean flow. Analytical expressions are derived for the transfer matrices.