Stability of a compressible laminar wall-jet with heat transfer

The flow of a plane, laminar, subsonic perfect gas wall jet with heat transfer through the wall was investigated theoretically. For the case under consideration the entire surface was maintained at a constant temperature which differed from the temperature of the ambient gas. The velocity and temperature distribution across the flow were calculated for a variety of temperature differences between the ambient gas and the surface. The boundary layer equations representing these flows were solved by using the Illingworth-Stewartson transformation, thus extending the classical Glauert's solution to a thermally non-uniform flow. The effects of heat transfer on the linear stability characteristics of the wall jet were assessed by making the local parallel flow approximation. Two kinds of unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. The influence of cooling or heating on the stability of the flow was expected in view of the experience accumulated in incompressible boundary layers, i.e. heating destabilizes and cooling stabilizes the flows. Cooling of the wall affects the small scale disturbances more profoundly, contrary to the results obtained for the large scale disturbances.