Abstract
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 Τc to mark the onset of convective instability is presented as a function of the Rayleigh number RaO and the Prandtl number Pr. The present stability analysis predicts that Τc decreases with increasing Pr for a given RaO. 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 Τ≏(2∼4) Τc .
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