Onset of buoyancy-driven convection in the horizontal fluid layer subjected to ramp heating from below

The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with a constant heating rate is analyzed by the propagation theory. Here the dimensionless critical time τ_c to mark the onset of convective motion is presented as a function of the Rayleigh number Ra_φ and the Prandtl number Pr. The present stability analysis predicts that for a given large Ra_φ, τ_c decreases with increasing Pr and it is independent of the conditions of the upper boundary. For deep-pool systems, the deviation of the temperature profile from conduction state occurs starting from a certain time τ_o≅4τ_c. The present predictions are compared with other models and existing experimental results in the whole time domain.