RESPONSE OF A CONFINED GAS TO A THERMAL DISTURBANCE .1. SLOW TRANSIENTS

The response of a perfect gas confined in a slot to a monotonically varying temperature disturbance at the boundaries is considered. On the acoustic-time scale of the slot the solution is described in terms of a thin expanding conduction boundary layer adjacent to the slot wall and an isentropic core in which a continuous system of acoustic waves propagate. The equations describing the heat transfer process on the longer conduction-time scale are found to include nonlinear convection and pressure work terms. Strong coupling exists between the induced velocity field arising from thermal expansion of the gas and the variation of thermodynamical variables. A weak acoustic field is found to be propagating in a spatially anisotropic system varying slowly in time. Solutions are developed by a variety of perturbation methods based on a small parameter which is the ratio of the acoustic to conduction time in the system.