Onset of Convection in Liquids Subjected to Transient Heating from Below

Experimental studies have been made of the onset of natural convection in liquids subjected to heating from below while insulated above. The temperature gradient necessary for convection to start was measured with a thermopile immersed in the liquid. When the liquids were not rotating, it was found that the temperature difference between the top and bottom surfaces required to initiate convection can be related with the heat input by the formula $$\mathrm{Ra}\text{=90.7\hspace{0.17em}(}\mathrm{Ra}·\mathrm{Nu}{)}^{\text{0.394}},\mathrm{Ra}\text{>1700,}$$ where Ra is the Rayleigh number, and Nu is the Nusselt number, both specially defined for the transient case. Mercury and silicone oil were used in the experiments without rotation. It was found in experiments with mercury, that in the range of Taylor numbers covered, the presence of spin increased the temperature difference required to initiate convection. The Rayleigh number necessary for the onset of fluid motion in spinning mercury is plotted as a function of the Taylor number for several values of the heat flux.