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 Marang oni 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 combustio n. 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 bo undary layers in a region around the heat source, while viscous forces exte nd 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 re maining thermocapillary stresses, in the case of axisymmetric thermocapilla ry flow; and by the horizontal gradient of a hydrostatic pressure distribut ion, in the case of buoyant flows. For large values of the Prandtl number, this region is followed by a region of viscosity-dominated flow which may b e responsible for a large fraction of the heat loss to the bottom. A linear stability analysis of the surface boundary layer in the vicinity of the he at source gives values of the critical Marangoni number for the transition to oscillatory flow that are comparable to known experimental results. (C) 2000 American Institute of Physics. [S1070-6631(00)00509-2].