Effect of Loss/Gain of Energy on Standing Oscillations in a Planar Resonator

The dynamics of small-magnitude acoustic perturbations in a planar resonator is considered. Fluid flow is affected by a heating–cooling function, which may disturb its adiabaticity. This concerns open flows with an external inflow of energy and flows with relaxation of thermodynamic processes, such as exothermic chemical reaction and excitation of vibrational degrees of freedom of a molecule. These processes make the flow acoustically active under some conditions. The heating–cooling function is supposed to depend on the thermodynamic parameters of the fluid. The dynamics of perturbations in the volume of a resonator is described analytically by the separation of variables in the wave equation with an account of proper boundary conditions. Some particular cases of the heating–cooling function allow us to describe a considerable deviation of the adiabaticity of the flow analytically.