Convection versus

Figure 5.34 Critical heat flux of boiling sodium under subcooled forced convection versus nonboiling convection heat flux. (From Lurie, 1966. Copyright 1966 by Rockwell International, Canoga Park, CA. Reprinted with permission.)...

Convection is driven by a pressure gradient, whereas diflhsion relies on a concentration gradient. The ratio of convection versus diffusion is defined as the Peclet number. In normal tissues, the Peclet number is, in general, less than unity for small and hydrophilic molecules and larger than unity for macromolecules. Thus, interstitial transport is dominated by diffusion for small molecules and convection for large ones. In solid tumors, the pressure gradient is low due to the uniformly elevated IFP as discussed above. Thus, the Peclet number may also be smaller than unity for macromolecules. In this case, the transport of macromolecules relies on diffusion as well. 

FIGURE 4.2 Convection versus diffusion, (a) Convective fluid transport in this system moves material from the upper tank to the lower tank, (b) A concentration gradient between white and gray particles results in net diffusive transport of gray particles to the left and white particles to the right. 

FIGURE 6.4 Schematic of natural convection versus forced convection. 

The lower Emit of applicability of the nucleate-boiling equations is from 0.1 to 0.2 of the maximum limit and depends upon the magnitude of natural-convection heat transfer for the liquid. The best method of determining the lower limit is to plot two curves one of h versus At for natural convection, the other ofh versus At for nucleate boiling. The intersection of these two cui ves may be considered the lower limit of apphcability of the equations. 

Figure 2.42 shows boiling curves obtained in an annular channel with length 24 mm and different gap size (Bond numbers). The heat flux q is plotted versus the wall excess temperature AT = 7w — 7s (the natural convection data are not shown). The horizontal arrows indicate the critical heat flux. In these experiments we did not observe any signs of hysteresis. The wall excess temperature was reduced as the Bond number (gap size) decreased. One can see that the bubbles grew in the narrow channel, and the liquid layer between the wall and the base of the bubble was enlarged. It facilitates evaporation and increases latent heat transfer. 

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...

Figure 11.14 E versus time curve recorded during the ORR on a FePc/C gas diffusion electrode j = —25 mAcm ). The FePc electrode was fed with ambient air without any convection (temperature 20 °C) [Baranton et al., 2005].

This value is close to the formal electrode potential and independent of the convection velocity. The plot of log(/d — j)/j versus E is linear with the slope nF/2.303RT. 

Similarly, in Figure 2.21, NR is plotted versus AT for boiling -pentate, benzene, and ethyl alcohol on a flat chromium surface (Cichelli and Bonilla, 1945). The value for m in all three cases was chosen to be 3. In the cases considered, the measured q" from experimental data was interpreted as "oil, neglecting the natural-convection contributions because the flux levels in the experiments were... 

The heat transfer from tubes in the freeboard was also measured for the 20 MW model. Figure 45 shows a comparison of the measured overall heat transfer coefficient in the 20 MW pilot plant versus that predicted from the scale model test. When the bed height is lowered, uncovering some tubes, the heat transfer is reduced because there are fewer particles contacting the tube surface. Although the scale model did not include proper scaling for convective heat transfer, the rate of change of the overall heat transfer should be a function of the hydrodynamics. 

However, the two mechanisms interact and molecular diffusion can reduce the effects of convective dispersion. This can be explained by the fact that with streamline flow in a tube molecular diffusion will tend to smooth out the concentration profile arising from the velocity distribution over the cross-section. Similarly radial dispersion can give rise to lower values of longitudinal dispersion than predicted by equation 4.39. As a result the curves of Peclet versus Reynolds number tend to pass through a maximum as shown in Figure 4.6. 

The multilayered Cu/Co systems discussed here can be grown as described next (6b). Electrolyte composition is based on a cobalt/copper ratio of 100 1 and consists of a solution of 0.34 M cobalt sulfate, 0.003 M copper sulfate, and 30g/L boric acid. The pH is fixed around 3.0, and there is no forced convection while deposition is carried out. The electrodeposition may usually be carried out potentiostatically at 45°C between —1.40 V versus SCE for the cobalt and —0.65 V versus SCE for the copper with an 3 cell potential interrupt between the cobalt-to-copper transition to avoid cobalt dissolution, which can occur when there is no interrupt. 

A major fallacy is made when observations obeying a known physical law are subjected to trend-oriented tests, but without allowing for a specific behaviour predicted by the law in certain sub-domains of the observation set. This can be seen in Table 11 where a partial set of classical cathode polarization data has been reconstructed from a current versus total polarization graph [28], If all data pairs were equally treated, rank distribution analysis would lead to an erroneous conclusion, inasmuch as the (admittedly short) limiting-current plateau for cupric ion discharge, albeit included in the data, would be ignored. Along this plateau, the independence of current from polarization potential follows directly from the theory of natural convection at a flat plate, with ample empirical support from electrochemical mass transport experiments. 

Nemes, C. and Laronze, J.Y., Trimolecular condensation of substituted indoles with paraformaldehyde and Meldrum s acid. Convective heating versus microwave irradiation a comparative study, Synthesis, 1999,254-257. 

This section analyzes the response of a charge transfer process under conditions of finite linear diffusion which corresponds to a thin layer cell. This type of cell can be achieved by miniaturization process for obtaining a very high Area/Volume ratio, i.e., a maximum distance between the working and counter electrodes that is even smaller than the diffusion layer [31], In these cells it is easy to carry out a bulk electrolysis of the electroactive species even with no convection. Two different cell configurations can be described a cell with two working electrodes or a working electrode versus an electro-inactive wall separated at distance / (see Fig. 2.23). 

Katz, M.M., Hargens, A.R. and Garfin, S.R. (1986) Intervertebral disc nutrition Diffusion versus convection. Clin Orthop, 243-245... 

Fig. 25 Convection, dispersion / diffusion, retardation and degradation of a species (single peak input) versus time along a flow path...

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