Uniform flux assumption

When the inlet assumptions state that water is entering the GDL at its interface with the catalyst layer, further clarification must be made between what has been called the uniform flux assumption and the uniform pressure assumption. The imiform flux assumption includes an individual source of liquid water for every inlet throat along the GDL/catalyst layer interface, while the uniform pressure assumption includes only a single source of liquid water that is connected to each inlet throat along the GDL/catalyst layer interface. Pltysically, the uniform pressure assumption assumes that there is a water cluster outside the GDL with negligible hydraulic resistance from one side to the other. Due to the microstracture of the catalyst layer, this scenario would approximate reality only if a pocket of liquid water could form between the catalyst layer and the GDL. Conversely, the uniform flux assumption assumes no hydraulic connectivity outside of the GDL between inlet locations. A compromise between these two assumptions was made by Hinebaugh and Bazylak in a 2D stmctured pore network model of GDL invasion, where the first row of pores and throats within the GDL is initialized as fully saturated. Similar to the uniform flux assumption, a liquid water source was... 

Assuming that the He production in the entire crust is balanced by degassing, an average continental crustal He flux of 2.8x10 ° atoms m s = 3.3x10 ° cm STP cm yr can be derived (O Nions and Oxburgh 1983). This flux may in some cases be useful to estimate the He accumulation rate, but it remains questionable whether the assumption of a uniform flux is justified (e.g., Castro et al. 1998b Ballentine et al. 2002 in this volume Ballentine and Burnard 2002 in this volume). Therefore, He accumulation usually provides only a qualitative timescale. 

Resonance absorption in closely packed assemblies. So far we have only treated the case in which the absorber lumps are so widely spaced that they do not interact with each other i.e., the distances between them are large compared to the moderator free path. An important generalization is the one to closely packed assemblies where this condition is not fulfilled. This case was first treated by Dancoff and Ginsburg [16]. The problem is solved in principle by a redefinition of the escape probability Pq, This quantity was defined as the probability that a neutron coming from a uniform source density in the absorber escapes from it, which means that for large separation of the absorber lumps it will make the next collision in the moderator. We now define an effective escape probability PJ for close assemblies, which means just the same, i.e., that a neutron bom with a flat distribution in an absorber makes its next collision in the moderator, excluding the cases in which, after traversal of one or more moderator sections, it collides inside another absorber lump. It is clear that under the flat-flux assumption, all previous formulas still hold when Pq is replaced by PJ, and it remains only to find appropriate expressions for the latter. 

Many additional studies have been conducted with the boundary layer model by taking into account the variation of physical properties with composition (or temperature) and by relaxing the assumption that Vy = 0 at y = 0 when mass transfer is occurring. Under conditions of high mass transfer rates one finds that mass transfer to the plate decreases the thickness of the mass transfer boundary layer while a mass flux away from the wall increases the boundary layer thickness The analogous problem of uniform flux at the plate has also been solved. Skelland describes a number of additional mass transfer boundary layer problems such as developing hydrodynamic and mass transfin- profiles in the entrance region of parallel flat plates and round tubes. 

We have used here Eq. (10.131) for Pe., and Mr Vrpy When these expressions are compared with (10.38) and (10.39), it is seen that the NR approximation for leads rather easily to a statement in the standard form. Note, however, that because of the flat flux assumption the present derivation does not contain the resonance disadvantage factor fr. This quantity is customarily computed using a one-velocity model to represent the entire fast-neutron population. It is well recognized that this point of view is crude and somewhat unclear. On the one hand, when used with the NR approximation, it may be observed that only one collision is required to remove a resonance neutron from the vicinity of a resonance thus the spatial distribution would be very nearly uniform and isotropic. On the other hand, if the NRIA approximation is valid, then the absorptions are necessarily very strong and the use of a disadvantage factor based on diffusion theory is not well justified. For these reasons it has been omitted in this treatment as an unwarranted refinement not in keeping with the precision of the over-all model. ... 

In practice the assumption of the uniform heat release per unit length of the rod is not valid since the neutron flux, and hence the heat generation rate varies along its length. In the simplest case where the neutron flux may be taken as zero at the ends of the fuel element, the heat flux may be represented by a sinusoidal function, and the conditions become as shown in Figure 9.20. 

The present model takes into account how capillary, friction and gravity forces affect the flow development. The parameters which influence the flow mechanism are evaluated. In the frame of the quasi-one-dimensional model the theoretical description of the phenomena is based on the assumption of uniform parameter distribution over the cross-section of the liquid and vapor flows. With this approximation, the mass, thermal and momentum equations for the average parameters are used. These equations allow one to determine the velocity, pressure and temperature distributions along the capillary axis, the shape of the interface surface for various geometrical and regime parameters, as well as the influence of physical properties of the liquid and vapor, micro-channel size, initial temperature of the cooling liquid, wall heat flux and gravity on the flow and heat transfer characteristics. 

We will adopt the assumption of thermal equilibrium under considered conditions of membrane operation this implies uniform temperature and zero heat flux in the system. 

A widely used method described by Shirley (1972) is similar, but it employs instead a summation over the observed electron flux (z)fc, which includes contributions from electrons already scattered. Our own iterative method is based on the assumption of uniform scattering of a fixed fraction of the electrons that would be observed in the complete absence of scat-... 

For radial concentration profiles, a quadratic representation may not be adequate since application of the zero flux boundary conditions at r, = cp0 and r, = 1.0 leads to d2 = d3 = 0. Thus a quadratic representation for the concentration profiles reduces to the assumption of uniform radial concentrations, which for a highly exothermic system may be significantly inaccurate. 

However, a quadratic representation of the radial concentration profile may not be adequate since application of zero flux conditions at the inner thermal well and outer cooling wall with a quadratic profile reduces to an assumption of uniform radial concentrations. Although additional radial... 

The thermal entrance region in a hydrodynamically fully developed flow in a rectangular duct may be studied by the use of the integral method. In this section, the uniform wall temperature and the uniform wall heat flux cases are discussed. The physical model is based on the following assumptions ... 

Consider developing fl/ w in a vertical wide channel when there is the same uniform heat flux, < . applied at each wall and w here the flow ent rs the channel at a temperature of T.. Write out the governing equations, clearly stating the assumptions on which these equations are based. Express the governing equations in dimensionless form, defining the dimensionless temperature as (7 - T,)k/qwW where Y is the width of the channel. Discuss how these equations can be numerically solved. 

One remark should be made. According to all the available theories the total pressure inside the septum should be uniform if the total pressures at its surfaces are equal. This is not the case for the BFM. However, the numerical solution of the problem shows that this total pressure variation can be neglected in the calculation of the fluxes and the assumption of a constant pressure over the septum made by Kerkhof [5] is correct. 

The first two terms represent the electron flux and the change in electron concentration with time, respectively. The third term represents the recombination rate and is assumed to be first order with electron density. The fourth term is the generation term that assumes the dye concentration is uniform throughout the film. Eq. 33 has been solved analytically. Sddergren and co-workers [155] have shown that the steady-state photocurrent is consistent with this model and the assumption that electron transport occurs by diffusion. 

SOLUTION The power consumed by the resistance wire of a hair dryer is given. The heat generation and the heat flux are to be determined. Assumptions Heat is generated uniformly in the resistance wire. 

Assumptions 1 Steady flow conditions exist. 2 The-surface heat flux is uniform. 3 The inner surfaces of the tube arc smooth,... 

SOLUTION Spray paint cans are temperature tested by submerging them in an uncovered hot water bath. The rates of heat loss from the top surface of the bath by radiation, natural convection, and evaporation are to be determined. Assumptions 1 The low mass flux conditions exist so that the Chilton-Colburn analogy between heat and mass transfer Is applicable since the mass fraction of vapor in the air is low (about 2 percent for saturated air at 300 K). 2 Both air and water vapor at specified conditions are ideal gases (the error involved in this assumption is less than 1 percent). 3 Water is maintained at a uniform temperature of 50°C. 

Hydrodynamically fully-developed laminar gaseous flow in a cylindrical microchannel with constant heat flux boundary condition was considered by Ameel et al. [2[. In this work, two simplifications were adopted reducing the applicability of the results. First, the temperature jump boundary condition was actually not directly implemented in these solutions. Second, both the thermal accommodation coefficient and the momentum accommodation coefficient were assumed to be unity. This second assumption, while reasonable for most fluid-solid combinations, produces a solution limited to a specified set of fluid-solid conditions. The fluid was assumed to be incompressible with constant thermophysical properties, the flow was steady and two-dimensional, and viscous heating was not included in the analysis. They used the results from a previous study of the same problem with uniform temperature at the boundary by Barron et al. [6[. Discontinuities in both velocity and temperature at the wall were considered. The fully developed Nusselt number relation was given by... 

Convective heat transfer analysis for a gaseous flow in microchannels was performed in [24]. A Knudsen range of 0.06-1.1 was considered. In this range, flow is called transition flow. Since the eontinuum assumption is not valid, DSMC technique was applied. Reference [24] considered the uniform heat flux boundary condition for two-dimensional flow, where the channel height varied between 0.03125 and 1 micrometer. It was concluded that the slip flow approximation is valid for Knudsen numbers less than 0.1. The results showed a reduction in Nusselt number with increasing rarefaetion in both slip and transition regimes. 

In ID models it is assumed that gases and potentials are uniformly distributed in the cell lateral cross section. Although this assumption may work in some fragments of the cell, on the scales of the whole cell it is far from real (cf. Fig. 19). There are two main factors that disturb uniformity. First, channels and ribs alternate along the y axis, that is, domains of fixed gas concentration and zero normal current alternate with domains of fixed potential and zero flux of gases. This leads to a complicated 2D field of concentrations and currents in a plane, perpendicular to the channel axis. Second, the feed gas is consumed as it moves along the channel, which leads to nonuniform along-the-channel distribution of local current density. Furthermore, the two effects are coupled with each other. 

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