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The convective instability in a plane liquid layer with time-dependenttemperature profile is investigated by means of a general method suitable forlinear stability analysis of an unsteady basic flow. The method is based on anon-normal approach, and predicts the onset of instability, critical wavenumber and time. The method is applied to transient Rayleigh-Benard-Marangoniconvection due to cooling by evaporation. Numerical results as well astheoretical scalings for the critical parameters as function of the Biot numberare presented for the limiting cases of purely buoyancy-driven and purelysurface-tension-driven convection. Critical parameters from calculations are ingood agreement with those from experiments on drying polymer solutions, wherethe surface cooling is induced by solvent evaporation.

Transient Rayleigh-Benard-Marangoni Convection due to Evaporation : a Linear Non-normal Stability Analysis