Effect of thermal boundary conditions on propagation of sound waves in a rarefied gas

Existing studies on sound wave propagation in rarefied gases examine sound generation by actuated boundaries subject to isothermal boundary conditions. We study the effect of replacing the isothermal conditions with heat-flux conditions (which are easier to implement in practice) on the propagation of sound. Towards this end, we consider the response of a rarefied gas, confined in an adiabatic (thermally insulated) channel, to instantaneous (small-amplitude) motion of its boundaries in the normal direction. The analytical problem is formulated and solved for an ideal monatomic gas at collisionless (highly rarefied) and continuum conditions, and the effect of heat-flux insulation is demonstrated through comparison with counterpart results obtained for a gas confined between isothermal walls. The results, found in quantitative agreement with numerical Monte Carlo simulations, motivate further study on the effect of heat injection at the boundaries on propagation of sound waves in the gas. It is demonstrated that heat "injection" or "suction" may be applied to achieve 'acoustic cloaking' of actuated boundaries, a much desired property in classical acoustics.