Energy Stability Analysis on the Onset of Buoyancy-Driven Convection in a Horizontal Fluid Layer Subject to Evaporative Cooling

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number Ra-c = 669 convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time tau(m) to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.