ABSTRACT
So far we have discussed various aspects of instability and receptivity of pure hydrodynamic flows whose linear dynamics can be followed by solving the fourth order Orr-Sommerfeld equation (OSE). If one includes any one of the effects due to compressibility, heat transfer or surface compliance, then the linear dynamics become more involved, as one needs to solve instead the sixth order OSE. This added complexity also enhances the flow instability, whether one is interested in linear analysis for small excitation amplitudes or for large amplitude excitations for which one would be required to solve the full Navier-Stokes equation. In the present chapter, the effect of heat transfer is studied from both linear and nonlinear perspectives, on instability. Also, focus is on mixed convection flow at low speed, which can be modeled by the Boussinesq approximation. One of the major difficulties of studying mixed convection flows is the lack of available canonical equilibrium flows, even when one is interested in flows past a flat plate. For a constant external flow past a horizontal flat plate, a similarity solution is available due to [315]. We will confine our instability and receptivity studies of this flow only, while reference is made to flow past a vertical plate whose mean flow is obtained by non-similar approaches. In the concluding remarks for this chapter, we will discuss another class of mean flows obtained in [240] which is a generalization of the similarity solution originally introduced in [315].
