Volume zone

On the basis of these principles, Novak and Gibbs (1971) proposed a map of compatible and ry dimensions for the formation of a garnet phase. This map (figure 5.15) shows that the commonly observed components plot in the low-volume zone of the compatibility area. Theoretically, compounds with higher volumes may form and remain stable at appropriate P and T conditions. 

Number of surface and volume zones in enclosure Partial pressure of species k, atm Number of WSGG gray gas spectral windows Total radiative flux originating at surface zone t, W Net radiative flux between zone t and zonej, W Temperature, K... 

FIG. 5-18 Four enclosure geometries characterized by two surface zones and one volume zone. (Marks Standard Handbook for Mechanical Engineers, McGraw-Hill, New York, 1999, p. 4-73, Table 4.3.5.)... 

Energy Balances for Volume Zones—The Radiation Source Term Reconsider a generalized enclosure with N volume zones confining a gray gas. When the N gas temperatures are unknown, an additional set of N equations is required in the form of radiant energy... 

The radiative source term is a discretized formulation of the net radiant absorption for each volume zone which may be incorporated as a source term into numerical approximations for the generalized energy equation. As such, it permits formulation of energy balances on each zone that may include conductive and convective heat transfer. For K—> 0, GS —> 0, and GG —> 0 leading to S —> On. When K 0 and S = 0N, the gas is said to be in a state of radiative equilibrium. In the notation usually associated with the discrete ordinate (DO) and finite volume (FV) methods, see Modest (op. cit., Chap. 16), one would write S /V, = K[G - 4- g] = Here H. = G/4 is the average flux... 

Two-zone model, M = 1, N = 1 A single volume zone completely surrounded by a single sink surface zone. 

The protein polysaccharide is hydrolyzed at 100-110° for 3 hours with N sulfuric acid, neutralized with baryta solution, filtered, and the filtrate concentrated to small volume. Zone electrophoresis in borate buffer (pH 8.6) is then carried out for a suitable time, and the paper strip is dried and sprayed with ninhydrin (to locate the amino acids) and with aniline hydrogen phthalate (to detect the reducing sugars). 

Energy Balances for Volume Zones—The Radiation Source Term. . 5-35... 

Diagonal matrix of gray gas WSGG volume zone... 

The radiative source term is a discretized formulation of the net radiant absorption for each volume zone which may be incorporated as a source term into numerical approximations for the generalized energy equation. As such, it permits formulation of energy balances on each zone that may include conductive and convective heat transfer. Eor K—> 0, GS —> 0, and GG —> 0 leading to S —> On. When and... 

Aniline, cyclohexylamine Commercial sweeteners UV-Vis 4 x 10 6, 8 x 10 6 mol L 1 150 Simultaneous determinations/sample "infinite volume"/zone stopping at the detector [136]... 

The latter occurs near 50 %. This step is associated with a decrease in the coefficient of diffusion. We have attributed this in part to the formation of water clusters within the periodically arranged free volume zones in the micofibril. 

A tissue volume zone proximal to M, with gradually reduced contribution (sensitivity) at increasing distance from M. 

Oxygen-consumption rate Settled sludge volume Zone settling rate Specific gravity(SG)... 

A large volume zone above the rinse sump allowing for rinsing with freshly condensed solvent (color code green),... 

Each gas volume zone, i, has a gas temperature Tg,i and each surface zone has a surface temperature T i. 

For volume zone, i, the balance equation expresses that the ineoming radiation flux from the other volume, 1, and surface zones, k, minus the adiation flux to the other gas and surface zones plus the net heat release is equal to zero. The net heat release in the zone includes the heat of combustion plus heating of the flue gas and minus heat delivered by convection to the adjaeent surface zones. A volume equation is then ... 

The eonvection heat transfer from the gas volume has of course only eontributions from the two neighbouring tube and furnace wall zones. The heat release in a volume zone Qcomb is from the eombustion. For a sidewall-fired reformer it can be ealeulated eonsidering the burner as a point source [352] [358] or simply as a duty heat release in the nearby gas volume assuming a well-stirred combustion. For a top-fired furnace an appropriate duty heat release model must be used. 

The circumferential strip of the kiln freeboard (Figure 7.13) is isolated and subdivided in N small area elements. The portion of the kiln freeboard, approximately three kiln inside diameters in each axial direction viewed by these area elements, is subdivided into volume zones such as Vj comprising the freeboard gas, and the surface zones such as Aj that form the exposed bed and wall surfaces. The exchange areas between each of the zones and the elements of the circumferential strip are then evaluated and used to calculate the radiation streaming to these elements from the various volumes and surface zones, either directly or after undergoing one or two reflections. 

For the calculation of the global radiative heat transfer from the furnace to the reactor, the former is divided into isothermal surface and volume zones (Fig. 12.5.A-2). Because of the symmetry, only one fourth of the furnace has to... 

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