Number Rayleigh

Rawwool Raybestos g-Ray detectors Ray diagram Rayleigh number Rayleigh scatter Rayleigh scattering... 

Figure 2. Schematic of typical data and consistent Poincare sections from the quasiperiodic regime of Rayleigh-B nard convection. The rotation number W (in arbitrary units) is plotted versus Rayleigh number R for two different values...

Turbulent free convection attracted early attention in limiting-current studies, because the laminar, free convection boundary layer at a vertical plate becomes turbulent at a height characterized approximately by the Rayleigh number... 

At low Rayleigh numbers, Wragg (W6) found a smaller Ra dependence, resembling more the dependence in laminar free convection. In this range of Ra numbers, a cellular flow pattern is believed to exist, analogous to that of thermal and surface tension-driven cellular convection (Benard cells F3). In the range where the convection is turbulent, the Ra1/3 dependence has been confirmed over seven powers of Ra by Ravoo (R9), who used a centrifuge to vary the body force at constant bulk composition. 

Ra Rayleigh number defined by Eq. A Difference of an electrolyte property... 

In all these expressions, the group Gr Pr occurs, and this is often referred to as the Rayleigh number. 

The Frank-Kamenetskii theory has been extended to allow for reactant consumption [16—18], other geometries [19, 20] and heat transfer by convection as well as conduction, this being particularly important in gaseous systems when the Rayleigh number Ra > 600 [21]. ... 

One can describe these phenomena through the Reynolds number (forced convection) and Rayleigh number (natural convection), but the reader can see immediately that the situations are so complicated that correlations in elementary texts on fluid flow are not easily applicable to predicting flame behavior. Reactive flows are among the most complex problems in modem engineering. 

We consider either isothermal mass transfer (Gq == 0) or uniform composition heat transfer (Gr = 0) from a particle with constant surface composition or temperature. The Rayleigh number Ra is used for both GqPr and Gr Sc. 

The boundary layer equations for an axisymmetric body, Eqs. (1-55), (10-17), and (10-18) have been solved approximately for arbitrary Sc (L4). For Sc oo the mean value of Sh can be computed from Eq. (10-20). Solutions have also been obtained for Sc oo for some shapes without axial symmetry, e.g., inclined cylinders (S34). Data for nonspherical shapes are shown in Fig. 10.3 for large Rayleigh number. The characteristic length in Sh and Ra is analogous to that used in Chapters 4 and 6 ... 

For shapes which have an appreciable fraction of area over which the normal component of the buoyancy force is directed away from the surface (e.g., a heated horizontal plate facing upward) the turbulent regime where SF oc (Ray occurs at low Ra. For example, the horizontal plates of Fig. 10.3 have only one side exposed, the side for which the normal component of buoyancy is directed away from the plate. Here the power relation applies at Ra > 10. For horizontal cylinders, on the other hand, such a relationship is exhibited for Ra > 5 X 10. For spheres in Fig. 10.2, there is no indication of this transition even at Ra = 10. The critical Rayleigh number, Ra/, above which the j-power relationship applies is correlated by... 

There are several correlations. One is based on the Rayleigh number, valid for bubbles of less than 2.5 mm (spherical bubbles)... 

BENARD CONVECTION CELLS. When a layer of liquid is heated from below, the onset of convection is marked by the appearance of a regular array of hexagonal cells, the liquid rising in the center and falling near the wall of each cell. The criterion for the appearance of the cells is that the Rayleigh number should exceed 1700 (for rigid boundaries). 

The pictures are taken at various times during the translation of the ampoule through the furnace and thus correspond to different lengths of the melt. The intensity of the convection scales with the thermal Rayleigh number (Rat) for the vertical cylinder is given by... 

In the first case (Figure 8a), the side walls are adiabatic, and the reactor height (2 cm) is low enough to make natural convection unimportant. The fluid-particle trajectories are not perturbed, except for the gas expansion at the beginning of the reactor that is caused by the thermal expansion of the cold gas upon approaching the hot susceptor. On the basis of the mean temperature, the effective Rayleigh number, Rat, is 596, which is less than the Rayleigh number of 1844 necessary for the existence of a two-dimensional, stable, steady-state solution with flow in the transverse direction that was computed for equivalent Boussinesq conditions (188). 

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