The past efforts on the use of linear Taylor instability theory to predict heat transfer and minimum heat flux during film boiling on flat plates are briefly reviewed. This is followed by a review of recent work on numerical evaluation of non-linear growth of the interface between superposed layers of immiscible fluids. In these studies the numerical results were obtained for the temporal and the spatial variation of the heat transfer rate and the interface shape during saturated film boiling on a horizontal surface at low and near critical pressures, and during melting of a substrate supporting a pool of warmer liquid. New physical insights gained from the analysis are discussed.

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