Convective mixing functions

Oven Heaters. Each heater s thermal output is sensed via a thermocouple, which is used to close the loop to the heater controller. In larger, production-worthy systems, heaters are located both above and below the plane of the circuit board and are at least as wide as the conveyor. Thermal uniformity across a 60 cm tunnel width can be better than 2°C on top-of-the-line ovens. This is a function of the tunnel insulation, heater performance, heater control, and convective mixing of the heated air or gas. 

Fig. 3. Abundances within the hydrogen-burning shell as function of relative mass 5m, defined as ranging from 0 to 1 between the bottom of the shell and the convective envelope. From observational evidence a penetration of extra-mixing down to 5m 0.15 has been inferred...

Note that we have used the fluid velocity U to describe convection of particles, which is valid for small Stokes number. In most practical applications, / is a highly nonlinear function of c. Thus, in a turbulent flow the average nucleation rate will depend strongly on the local micromixing conditions. In contrast, the growth rate G is often weakly nonlinear and therefore less influenced by turbulent mixing. 

The 13C source liberates neutrons as soon as the 13C pocket is mixed into the hot convective shell (typically at Tcsb 150-108 K). The release of neutrons is essentially immediate, depending only upon the abundance of l3C in the shell and not on shell temperature. The abundance of 13C in the shell is a function of the small amount of 1H that was mixed into a 12C-rich region (which occurred - 105 years earlier) and thus Nn from the 13C source is mixing dependent, not temperature... 

Both the data in Table 1 and the surface Q(u,D) in Fig. 3 illustrate well that the sensitivity of the objective function with respect to the convective flow velocity is significant. At the same time, variation of Q as a function of the axial dispersion coefficient seems to be smaller, which means that the mean residence time has stronger influence on the properties of the particulate product than the axial mixing of particles. 

In measuring diffusion in liquids or gases, mixing by convection must be excluded. Several experimental arrangements are described, for example use of a diffusion tube, a diaphragm or a capillary. Measurement of the diffusion coefficient of pH-sensitive species as a function of pH allows conclusions with respect to the size of the species. 

Figure 4. Comparison of the oxygen yield Mo as a function of the initial stellar mass Mzams for models with and without stellar wind mass loss, and assuming a remnant mass of the order of 2Mq. Upper panel Models with slow semiconvective mixing. Weaver Woosley s (1993 WW93) models are computed without mass loss, Langer Henkel (1995 LH95) included mass loss. Lower panel Models with fast semiconvective mixing resp. Schwarzschild criterion for convection. Woosley Weaver (1995 WW95) neglected mass loss, Maeder (1992 M92) explored models with standard and excessive mass loss.

Equation 2.20 is the advection-dispersion (AD) equation. In the petroleum literature, the term convection-diffusion (CD) equation is used, or simply diffusion equation (Brigham, 1974). When a reaction term is included, the term advection-reaction-dispersion (ARD) equation is used elsewhere. When the adsorption term is expressed as a reaction term, the ARD equation is as discussed later in Section 2.4. Several solutions of Eq. 2.20 have been presented in the literature, depending on the boundary conditions imposed. In general, they are various combinations of the error function. When the porous medium is long compared with the length of the mixed zone, they all give virtually identical results. 

Liquid mixing in bubble columns is a result of global convective re-circulation of the liquid phase and turbulent diffusion due to eddies generated by the rising bubbles. By structuring the gas and the liquid flow, HyperCat reduces the axial dispersion for both phases leading to a large reduction in axial dispersion coefficients (Dax)- The real benefit of this reduced dispersion is that it is not a function of the colunm diameter (Dc) as is the case with conventional bubble colunm reactors. 

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