Steady thermocapillary-buoyant flow in an unbounded liquid layer heated nonuniformly from above

Thermocapillary and buoyant flows induced by nonuniform heating of the free surface of a horizontally unbounded liquid layer over a cold solid bottom are studied numerically and by order of magnitude analyses for large Marangoni and Rayleigh numbers. The Prandtl number of the liquid is assumed to be of order unity or large, which are the cases of most interest in combustion. The asymptotic structures of plane and axisymmetric stationary flows are described qualitatively, showing that they consist of several horizontally spaced regions. Heat conduction and viscous forces are confined to thin boundary layers in a region around the heat source, while viscous forces extend to the whole liquid layer in a longer region where the flow is driven by the momentum imparted to the liquid by thermocapillary stresses around the source, in the case of plane thermocapillary flow; by this momentum and remaining thermocapillary stresses, in the case of axisymmetric thermocapillary flow; and by the horizontal gradient of a ...