The response of a confined gas to a thermal disturbance: rapid boundary heating
The authors employ concepts developed by the second author [SIAM J. Appl. Math. 36, 624 ff. (1979)] to study the mechanical response of a gas in a slab when boundary heating occurs on the acoustic-time scale of the container. During that period the energy addition at the boundary is of the order \(10^ 6\) larger than that considered in the above paper. As a result the acoustic field generated by the boundary-layer gas expansion is a similar factor larger. In fact the velocity field associated with the acoustic process is a factor of \(10^ 3\) larger than that associated with bulk gas deformation during the longer conduction-dominated process. The acoustic field retains its linear character because the power added of the boundary is not large enough to drive an acoustic wave front which becomes nonlinear within the finite dimension of the slab. Numerical solutions for the nonlinear heat-transfer process, which includes gas deformation, are obtained to show, now the system relaxes to the final steady state. Flow reversal is observed as density variations are smoothed out.
scientific article; zbMATH DE number 3900405