The stability of the heated plane Poiseuille flow subjected to a uniform crossflow

• The crossflow modifies the basic flow field of the heated plane Poiseuille flow.
• The symmetry of the flow is broken.
• The onset of instability of the basic flow is affected by the direction and magnitude of the cross flow, and it also depends upon the Prandtl number of the fluid.
• The rate of heat transfer at the boundary, where the fluid is injected into the layer, gets decreased.

The Poiseuille flow of an incompressible viscous fluid confined between two parallel porous horizontal walls, and subjected to an adverse temperature gradient, is studied numerically. A uniform crossflow is considered across the fluid layer. The crossflow modifies the velocity field and the temperature field in the basic state which affects the onset of the instability. The stability of the basic state is discussed with respect to the Rayleigh number at the fixed small values of the Reynolds number and with respect to the Reynolds number at the fixed values of the Rayleigh number. The crossflow is found to stabilize or destabilize the basic state, depending upon its magnitude and direction. The onset of instability also depends upon the Prandtl number of the fluid.