Mass flux number

Particle or mass flux Number of particles or mass of substance crossing a unit surface per unit time. The appropriate units (SI) are particles m 2s 1 or kg m 2s 1, but particles cm 2s 1 or g cm-2s—1 are often used. Total mass flux of a substance (emitted, for example, at the Earth s surface) is often expressed in Tg yr-1 (1012 g yr 1). 

Solution of Eq. (6-114) for G and differentiation with respect to p reveals a maximum mass flux = P2VMJ RT) and a corresponding exit velocity and exit Mach number Mo = L/. This... 

The exit Mach number Mo may not exceed unity Mo = 1 corresponds to choked flow sonic conditions may exist only at the pipe exit. The mass velocity G in the charts is the choked mass flux for an isentropic nozzle given by Eq. (6-118). For a pipe of finite length. 

Equation (6-128) does not require fric tionless (isentropic) flow. The sonic mass flux through the throat is given by Eq. (6-122). With A set equal to the nozzle exit area, the exit Mach number, pressure, and temperature may be calculated. Only if the exit pressure equals the ambient discharge pressure is the ultimate expansion velocity reached in the nozzle. Expansion will be incomplete if the exit pressure exceeds the ambient discharge pressure shocks will occur outside the nozzle. If the calculated exit pressure is less than the ambient discharge pressure, the nozzle is overexpanded and compression shocks within the expanding portion will result. 

Fig. 5.46 A plot of the experimentally determined heat transfer coefficient as a function of the superficial gas velocity and the gas Reynolds number. The liquid mass fluxes are 78.6 and 290 kg/m s, the heat fluxes are 20 and 33 kW/m and the pressure ranges from 140 to 200 kPa. Reprinted from Bao et al. (2000) with permission...

Number Heat flux q Mass flux G Bubble Parameter... 

In Fig. 5.5, the flow configuration and velocity and temperature distributions at the time instant of 12.5 s are depicted. Even though the flow is subsonic, due to the high Reynolds number, the flow structure in the region upstream of the solid propellant is minimally affected by the time-dependent boundary shape due to phase change. However, the thermal characteristics near the propellant interface show clear signs of time dependency, indicating that the mass flux of... 

The mass flux can also be expressed as a function of Mach number using Eqs. (1.25) and (1.26) as follows ... 

Na Molar flux of A with respect to stationary axes (see Table III) (40) nA Mass flux of A with respect to stationary axes (see Table III) n Number density (number of molecules per unit volume) (86)... 

The derivation of the two-box model follows naturally from the one-box model. It is useful for describing systems consisting of two spatial subsystems which are connected by one or several transport processes. The mass balance equations for the individual boxes look like Eq. 21-1 with the addition of terms describing mass fluxes between the boxes. Each box can be characterized by one or several state variables. Thus, the dimension of the system of coupled differential equations is the product of the number of boxes and the number of variables per box. 

The blocks of the block-tridiagonal structure correspond to the mesh, with each block being a square matrix with the dimension of the number of dependent variables at each mesh point (here the number of species, plus temperature, plus the mass flux). 

It is probably clear that any number of performance indexes can be written by comparing the various mass fluxes. The important point is that for the stagnation-flow geometries, all the mass fluxes can be written per unit surface area. Thus the indexes, which are ratios of fluxes, are independent of reactor size, so long as the reactor preserves the desirable similarity behavior. It is also important to note that these effectiveness indexes can be derived from the one-dimensional similarity simulations that consider the detailed chemical reaction behavior. 

As flow velocity is increased, the emitted mass flux increases. In fact, the number of taking-off possibilities equals the number of boxes at the bed surface times the number of time step of the model. Moreover, the number of boxes at the bed surface multiplied by the number of time step is proportional to U. ... 

Example 7 Flow through Frictionless Nozzle Air at p0 and temperature T0 = 293 K discharges through a frictionless nozzle to atmospheric pressure. Compute the discharge mass flux G, the pressure, temperature, Mach number, and velocity at the exit. Consider two cases (l)p0 = 7 X 105 Pa absolute, and (2) p0 — 1-5 x 10s Pa absolute. 

Other criteria can be used to establish the extinction condition and that are partially equivalent to the critical Damkohler number. Such criteria are a critical mass transfer numbers (BCI) [21,32], critical mass flux of fuel [2,6,28] or critical temperatures (Ta) [2,5,29-31], The critical mass transfer number has a direct influence over the flame temperature, and thus, represents the link between the condensed phase (i.e., production of fuel) and the chemical time. The critical mass flux operates under the same principle, but assumes a consistent heat input. Combustion reactions generally have high activation energy, therefore, the reaction can be assumed to abruptly cease when the temperature reaches a critical value (Tcr). 

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