On the stability of thermally stratified plane Poiseuille flow

The stability of thermally stratified plane Poiseuille flow is considered with respect to small disturbances. The interaction between the usual Tollmien-Schlichting type of instability and the thermal type of stability or instability is analyzed for different values of the Prandtl number. The problem is solved as an eigenvalue problem. The most important features from the results are that the critical Rayleigh number is found to be nearly linearly dependent on the Prandtl number, and that a critical Reynolds number always exists, no matter how much the fluid is stabilized by a linear temperature profile.