Convection regime

Fleury and coworkers showed that cellular electrokineitc flow occurs under some conditions at the tips of the branches in the binary-electrolyte thin-layer experiments [37, 38], They constructed a model based on point charges at the growth tips to account for the shape of the induced convection cells. The streamlines of these cells form arcs between adjacent branches. By comparing deposits formed under an electrokineitc regime with deposits formed under a free-convection regime, Barkey et al. 

To treat current distribution in through-holes, Hazlebeck and Talbot [140] formulated a model and established dimensionless criteria for ohmic and convective regimes. The most uniform distribution is obtained in the ohmically limited regime bounded by a numerical criterion based on a Peclet number and a Thiele modulus yT. In the notation of Takahashi and Gross,... 

Kondo and co-workers have studied through-mask deposition in the convective regime experimentally for both low [141] and high [142] Peclet numbers. They have also developed a numerical model which incorporates fluid flow [143], Their Peclet number is defined in terms of the cavity depth and has the same form as Eq. (6.12). They considered the effects of cavity geometry as determined by aspect ratio and sidewall angle. 

Gases are likely to be in the dispersion regime, not the pure convection regime. Liquids can well be in one regime or another. Very viscous liquids such as polymers are likely to be in the pure convection regime. If your system falls in the no-man s-land between regimes, calculate the reactor behavior based on... 

In the pure convection regime (negligible molecular diffusion) each element of fluid follows its own streamline with no intermixing with neighboring elements. In essence this gives macrofluid behavior. From Chapter 11 the conversion expression is then... 

Kimura, S. and Bejan, A., The Boundary Layer Natural Convection Regime in a Rectangular Cavity with Uniform Heat Flux From the Side , J. Heat Transfer, Vol. 106, pp. 98-103, 198 . 

Allegre C. J. (1997) Limitation on the mass exchange between the upper and lower mantle the evolving convection regime of the Earth. Earth Planet. Set Lett. 150, 1-6. 

If forced convection is controlling equation 13 will not correlate the data. In the forced convection regime, the Grashof number is unimportant and the general expression is reduced to. 

The domain of the mixed convection regime depends on the fluid the flow configuration and the flow pattern (17). It is usually defined by a region a < Gr/Re < b where a and b are the lower and upper bounds of the domain respectively and Gr/Re is the buoyanct force parameter n being a constant that varies with the flow configuration. Conversely when the buoyant force is the dominant mode of transport Re /Gr or some power of it becomes the important parameter for mixed convection. 

In a cold wall reactor, the convection regime is mixed. On the one hand, the temperature gradient between the substrate and the walls of the reactor tends to establish a system of natural convection (laminar flow). On the other hand, the flow of gas induces a forced convection (turbulent flow). A laminar flow is necessary to ensure a good uniformity of the epitaxial film thickness. 

The distribution of a decaying scalar field advected by a turbulent flow was studied by Corrsin (1961) who generalized the Obukhov-Corrsin theory of passive scalar turbulence for the linear decay problem F(C) = S(x) — bC. As in the case of the passive non-decaying scalar field, depending on the length scales considered, one can identify inertial-convective and viscous-convective regimes with qualitatively different characteristics. 

The mean heat transfer in the mixed convection regime for assisting flows has been correlated by Churchill [55] using the equation... 

Horizontal Flow. For laminar flow over the upper surface of a horizontal heated plate (or over the bottom surface of a cooled plate), the center of the mixed convection regime can again be estimated by equating the forced convection Nusselt number from Eq. 4.154 to that for natural convection from Eq. 4.39c (for detached turbulent convection). This results in... 

The details of the flow in the mixed convection regime have been clarified by Gilpin et al. [113]. After an initial development of the laminar forced convection boundary layer, rolls with axes aligned with the flow appear at the location marked Onset in Fig. 46. These persist until the end of the transition regime, marked Breakup, after which the motion appears as fully detached turbulent natural convection flow. 

Horizontal Cylinders. For a heated horizontal cylinder in perpendicular cross flow, the angle of the approaching stream, ( > in Fig. 4.47, greatly affects the heat flow in the mixed convection regime. For ( > = 0 the forced flow assists the natural convection and the dependence of the average Nus-selt number on Re resembles path A in Fig. 4.44. For = 90° there is a sharper transition from natural to forced convection than when 4> = 0, while for opposed flow (( > = 180°) there is a minimum as shown by path B in Fig. 4.44. For a cooled cylinder the same description applies except that ( > is measured from the vertical axis extending upward from the cylinder. 

A procedure for calculating the heat transfer in the mixed convection regime for the problem has also been proposed by Morgan [198] on the basis of work of Borner [22] and Hatton et al. [131]. For a given Ra and Re, the value of Nuw is computed from Eq. 4.45. For the given Re, the constants a and n are chosen from Table 4.14. The value of Re,- is then found from Eq. 4.163 with Nuf = Nuw that is,... 

On the basis of data available up to 1964, Metais and Eckert [190] established the forced convection boundary of the mixed convection regime, and their results are presented in Fig. 4.50. The line was drawn where natural convection was thought to alter the heat transfer from that for pure forced convection by 10 percent. Figure 4.49 defines the nomenclature for this problem. 

Heat transfer relations in the mixed convection regime have been proposed by several investigators, but the equation proposed by Depew and August [74] appears to be most successful. This relation agrees with their measurements for water (Pr = 6.5), ethyl alcohol (Pr 15), and a glycerol-water mixture (Pr = 375), as well as with the data from other authors, to about 40 percent ... 

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