Abstract
Thermal capillary flows in thin layers, brought about by non-uniform heating of the free boundary, are investigated at high Marangoni numbers. Selfsimilar solutions of the non-linear boundary-layer equations are constructed under conditions of axial symmetry, and asymptotic formulae for the solutions are found for small and large values of the thickness of the layer. It is shown that the selfsimilar solutions may not be unique when the parameters of the problem have certain values. The buoyancy forces in an inhomogeneous fluid lead to the reinforcement or suppression of the flows or to the formation of reverse flows close to the free boundary. Selfsimilar solutions when there are thermal capillary effects present have been studied in /1–5/.
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