Convective limit, strongly

The advantage of the k-profile scheme is its treatment of the convective limit. Since convection implies strong vertical mixing that destroys vertical gradients, the calculation of vertical fluxes from gradient formulas becomes inaccurate. This problem is circumvented in the k-profile approach by a special term in the expression for the turbulent vertical tracer fluxes, ww(J), which is active in the convective case and redistributes the surface flux, ivx(O), of a tracer X over the surface boundary layer in depth d. 

But before the virtues of the results and the approach are extolled, the method must be described in detail. Let us therefore return to a systematic development of the ideas necessary to solve transport (heat or mass transfer) problems (and ultimately also fluid flow problems) in the strong-convection limit. To do this, we begin again with the already-familiar problem of heat transfer from a solid sphere in a uniform streaming flow at sufficiently low Reynolds number that the velocity field in the domain of interest can be approximated adequately by Stokes solution of the creeping-flow problem. In the present case we consider the limit Pe I. The resulting analysis will introduce us to the main ideas of thermal (or mass transfer) boundary-layer theory. 

In Table 1 are shown a number of stars that have large Li abundances and rotational velocities. Are indicated both the measured rotational velocities and the limiting rotational velocity beyond which Li should be strongly depleted by the mechanism just described. These contradict the model just described. They require that the penetration of the convection zone by meridional circulation be at most partial. 

We may rule out all methods which depend upon ignition of the gases with electrically heated wires, heated spheres, or heated rods. These are kinetically unreliable, as they depend strongly on convective heat and mass transfer, they often act catalytically, and accurate temperature measurement is difficult. The following methods have found wider use in the plotting of explosion limits. 

To conclude the discussion on quasi-reversible reactions, we now direct our attention to sonoelectrochemical reactions on diamond electrodes [107-109], In sonoelectrochemistry, power ultrasound is applied to electrochemical cell, causing forced convection in the electrode-electrolyte system. As a result of the enhanced mass transfer, non-steady-state potentiodynamic curves with current peak turn to steady-state curves with a limiting current plateau (Fig. 21). Notice a significant increase in the current. It must be emphasized that in sonoelectrochemistry electrode materials are exposed to extreme conditions with mechanical strains induced by pressure waves and cavitation-induced liquid jets strong enough to cause severe erosion. Diamond withstands the sonoelectrochemical conditions perfectly. This opens up fresh possibilities for efficient electrolyses and electroanalyses with diamond electrodes. 

Our discussion of film condensation so far has been limited to exterior surfaces, where the vapor and liquid condensate flows are not restricted by some overall flow-channel dimensions. Condensation inside tubes is of considerable practical interest because of applications to condensers in refrigeration and air-conditioning systems, but unfortunately these phenomena are quite complicated and not amenable to a simple analytical treatment. The overall flow rate of vapor strongly influences the heat-transfer rate in the forced convection-condensation system, and this in turn is influenced by the rate of liquid accumulation on the walls. Because of the complicated flow phenomena involved we shall present only two empirical relations for heat transfer and refer the reader t.o Rohsenow [37] for more complete information. 

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