On the Shear Instability in Heated Poiseuille–Couette Flow in an Inclined Fluid Layer

In the current study, we examine the linear instability in Poiseuille flow of an incompressible viscous fluid confined between two parallel inclined planes. We study the impact of the temperature gradient and the superimposed Couette flow on the onset of shear instability in Poiseuille flow in the form of Tollmien–Schlichting (TS) waves. The role of the inclination of the fluid layer and the Prandtl number of the fluid on the onset of TS instability is observed to be significant in the presence of the temperature gradient, indicating the complex interplay between the thermal effects, the fluid properties, and the geometric factors.