Transient thermocapillary convection flows in a rectangular cavity with an evenly heated lateral wall

Transient thermocapillary convection flows driven by the evenly heated lateral wall of a rectangular cavity for zero-gravity condition are investigated by scaling analysis and numerical simulation. Scaling analysis suggests a set of flow regimes in different dynamical evolutions of the surface flow, dependent on Marangoni and Prandtl numbers and aspect ratios. In the typical case, the surface flow may travel, for example, under flow regimes of unsteady inertial-thermocapillary balance, unsteady viscous-thermocapillary balance, and steady viscous-thermocapillary balance in different dynamical evolutions. Additionally, scaling laws of the thickness and velocity of transient thermocapillary convection flows under different flow regimes have been obtained. Furthermore, two-dimensional numerical simulation has been performed. The numerical results show good agreement with the corresponding scaling predictions.