The onset of convective instability in a horizontal fluid layer subjected to a constant heat flux from below

The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer confined between the two infinite horizontal plates is analyzed by using propagation theory. For the system heated rapidly from below with a constant heat flux, the dimensionless critical time τc to mark the onset of convective instability is presented as a function of the Rayleigh number and the Prandtl number. The present predictions show that τc decreases with increasing Prandtl number for a given Rayleigh number. Available experimental data for water and silicone oil indicate that visible motion is detected first and then, an obvious deviation of the heated surface temperature from its conduction solution occurs. The difficulty of defining the detection time of visible motion is discussed in comparison with experiments.