Onset of buoyancy-driven convection in the horizontal fluid layer heated from below with time-dependent manner

The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with time-dependent manner is analyzed by using propagation theory. Here the dimensionless critical time tau(c) to mark the onset of convective instability is presented as a function of the Rayleigh number Ra-phi and the Prandtl number Pr. The present stability analysis predicts that T decreases with increasing Pr for a given Ra-phi. The present predictions compare reasonably well with existing experimental results. It is found that in deep-pool systems the deviation of temperature profiles from conduction state occurs starting from a certain time tau congruent to (2 similar to 4)tau(c).