(108e) The Onset of Buoyancy-Driven Convection in a Horizontal Fluid Layer Heated Isothermally from below

The convective motion and heat transfer characteristics are analyzed theoretically when an initially quiescent fluid layer confined between two horizontal plates is heated from below. It is well known that convective motion sets in for the Rayleigh number Ra ≥ 1708 in case of isothermal heating with rigid-rigid boundaries. Here three characteristic times t_c, t_D and t_u are clarified, which represent the time to mark the onset of intrinsic instability, the detection time of motion, and the undershoot time in the plot of the heating rate versus time, respectively. These characteristic times are investigated by employing the finite volume method under the single mode of instabilities. The stability criterion we are developing (refer to AIChE J. 2006, 52, 2677) is tested on the basis of temperature fluctuations. Their maximum, average and growth rate are examined with time. Based on the transient growth rates, it is found that t_c is the invariant but the predicted t_D- and t_u-values are dependent upon the magnitude of initial conditions forced. For large-Prandtl-number systems, numerical predictions agree well with the available experimental t_u-values for Ra > 10⁵ and the relation of t_u ≈ 7t_c. It is believed that t_D is located between t_c and t_u. This means that some growth period is required until the motion is detected. Also, the surface renewal theory combined with the boundary-layer instability model is applied in order to analyze turbulent heat transfer characteristics in the fully developed state. The resulting Nusselt number agrees well with available experimental data.