Stationary velocity and pressure gradients in a thermoacoustic stack

The second-order time-averaged acoustics of a viscous, thermally conducting gas between closely spaced parallel plates is studied. The acoustic disturbance is studied by expanding the equations of fluid dynamics and heat transfer to second order in Mach number. The undisturbed state is allowed to have a nonzero temperature gradient. A set of coupled equations for the time-averaged pressure gradient, velocity, and temperature are obtained and solved. Particular attention is paid to the relation between the time-averaged mass flux and pressure gradient. An explicit expression is obtained relating the time-averaged pressure drop across a thermoacoustic stack to the time-averaged mass flux through the stack.