A method for the efficient cooling of a cavity-bearing surface is disclosed. The method includes the provision of an extra-fine coolant mist to the surface to be cooled wherein the surface has at least two projections and at least one cavity therebetween. The mist is deposited so as to form an ultra-thin coolant film upon the surface and at least one coolant mist vortex within the cavity. The film is evaporated from its outside surface.
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