Linear stability analysis of Poiseuille–Bénard–Marangoni flow in a horizontal infinite liquid film

We present the first linear stability analysis of a Poiseuille–Bénard–Marangoni flow, which refers to a horizontal infinite liquid film flowing in one direction with uniform heating from below. This study concerns the two limiting cases of pure buoyancy effect (Ma = 0) and pure thermocapillary effect (Ra = 0). The stability thresholds of the flow and their variation with the control parameters (Biot, Reynolds and Prandtl numbers) are given and compared with those for a Poiseuille–Rayleigh–Bénard flow. The spatial structures of the flow are presented, and it is shown that the centers of the rolls are shifted upwards compared to the PRB case and that there is a loss of symmetry with respect to the vertical axis for the transverse rolls. These effects are directly linked to thermocapillary convection.