Continuous surfaces

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... 

FIG. 6 48 Continuous surface a) continuous flat surface, (h) continuous cylindrical surface. (From Sakiadis, Am. Inst. CLem. Eng. J., 7, 221, 467 [19611)... 

Continuous Cylindrical Surface The continuous surface shown in Fig. 6-48b is apphcable, for example, for a wire drawn through a stagnant fluid (Sakiadis, AIChE ]., 7, 26-28, 221-225, 467-472 [1961]). The critical-length Reynolds number for transition is Re = 200,000. The laminar boundary laver thickness, total drag, and entrainment flow rate may be obtained from Fig. 6-49 the drag and entrainment rate are obtained from the momentum area 0 and displacement area A evaluated at x = L. 

The laminar boundary layer on deforming continuous surfaces with velocity varying with axial position is discussed by Vleggaar... 

Figure 10-10E. A cutaway section of plate-type fins showing the continuous surface contact of the mechanically bonded tube and fins. (Used by permission The Trane Co., La Crosse, Wis.)...

In the case of alloys having one constituent considerably more reactive to oxygen than the others, conditions of temperature, pressure and atmosphere may be selected in which the reactive element is preferentially oxidised. Price and Thomas used this technique to develop films of the oxides of beryllium, aluminium, etc. on silver-base alloys, and thereby to confer improved tarnish resistance on these alloys. If conditions are so selected that the inward diffusion of oxygen is faster than outward diffusion of the reactive element, the oxide will be formed as small dispersed particles beneath the surface of the alloy. The phenomenon is known as internal oxidation and is of quite common occurrence, usually in association with a continuous surface layer of oxides of the major constituents of the alloy. 

Continuous, surface blowdown arrangements employ a multistage nozzle valve that permits the BW to expand and flash gradually and safely across each successive orifice and chamber with almost no noise. This effect reduces the flow velocity and virtually eliminates the risk of wire drawing. The BD valve is provided with a regulating lever and calibrated dial (or an electric actuator) for either manual or automatic BD rate adjustment. Continuous blowdown arrangements are entirely suitable for incorporation into FSHR systems. They are commonly employed for WT boilers. 

The isotropic form has little graphitic characteristic and essentially no optical activity. It is composed of very fine grains without observable orientation and for this reason, it is known as isotropic carbon rather than isotropic graphite. It is often obtained in fluidized-bed deposition, possibly due to continuous surface regeneration by the mechanical rubbing action of the bed. An isotropic structure, observed by transmission electron microscopy, is shown in Fig. 7.4.111]... 

Our interest is two-fold, we wish to know whether the defect is firstly structurally localised and secondly electronically locaHsed. Our second interest extends to know how important is the continuous surface arising from the spherical shape of Cea or the ellipsoidal shape of C o. 

One of the disadvantages of the method is that one must determine the smoothing parameter by optimisation. When the smoothing parameter is too small (Fig. 33.16a) many potential functions of a learning class do not overlap with each other, so that the continuous surface of Fig. 33.15 is not obtained. A new object u may then have a low membership value for a class (here class K) although it clearly belongs to that class. An excessive smoothing parameter leads to a too flat surface (Fig. 33.16b), so that discrimination becomes less clear. The major task of the... 

A dissociative adsorption of methanol forming surface methoxy groups is suggested as the initial step. This is followed by the slow step, the formation of some form of adsorbed formaldehyde species. Evidence.for the bridged species is not available, experiments with °0 labeled methanol are expected to clarify this. Continued surface oxidation leads to a surface formate group and to carbon monoxide. All the byproducts can be obtained by combination of the appropriate surface species. 

J. F. Place, R. M. Sutherland, and C. Dahne, Opto-electronic immunosensors A review of optical immunoassay at continuous surfaces, Biosensors I, 321-353 (1985). 

Myoglobin has five antigenic sites, each comprising a conformational 1y distinct continuous surface region of the polypeptide chain, and are situated on (Site 1) residues 16-21 1 or... 

From the definition of a particle used in this book, it follows that the motion of the surrounding continuous phase is inherently three-dimensional. An important class of particle flows possesses axial symmetry. For axisymmetric flows of incompressible fluids, we define a stream function, ij/, called Stokes s stream function. The value of Imj/ at any point is the volumetric flow rate of fluid crossing any continuous surface whose outer boundary is a circle centered on the axis of symmetry and passing through the point in question. Clearly ij/ = 0 on the axis of symmetry. Stream surfaces are surfaces of constant ij/ and are parallel to the velocity vector, u, at every point. The intersection of a stream surface with a plane containing the axis of symmetry may be referred to as a streamline. The velocity components, and Uq, are related to ij/ in spherical-polar coordinates by... 

From some point of ignition, a combustion wave spreads out until it forms a continuous surface over (he whole cross-section of the stream. The flame front is shaped by relative values of burning velocity and gas velocity. 

C did not puff when the products left the extruder die (Figure 15), These extrudates were recognized as "undertex-turzed". The common appearance of these undertexturized products was lack of smooth and continuous surface. A minimum temperature of 138°C was needed to produce puffed and retort-resistant extrudates when other process conditions were held constant. 

Figure 21.4—Method of factorial analysis using a singlefactor. If response (signal) consists of a continuous surface, the iso-response curves will lead to a variety of optimum situations.

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