Flux, defined

In addition to the particle settling velocity it is also necessary to know the corresponding rate at which mass is transferred during settling and this is best expressed as the mass flux defined by... 

We have designed, manufactured and tested a prototype that may be applied in thermal control of electronic devices. It was fabricated from a silicon substrate and a Pyrex cover, serving as both an insulator and a window through which flow patterns and boiling phenomena could be observed. A number of parallel triangular micro-channels were etched in the substrate. The heat transferred from the device was simulated by different types of electrical heaters that provided uniform and non-uniform heat fluxes, defined here respectively as constant and non-constant values... 

Returning to Eq. (166), the third term on the left-hand side involves the turbulent scalar fluxes, defined by... 

The heat flux transferred back from the gas phase to the burning surface is dependent on the temperature gradient in the gas phase, which is inversely proportional to the thickness of the reaction zone in the gas phase. Since the reaction in the gas phase is complete at the upper end of the bluish flame, the heat flux defined by Am conforms to the proportionality relationship Am l/6g p0- . The observed pressure dependence of the burning rate, is caused by the pressure depend-... 

These link regions, which we can identify with chemical bonds, are characterized by the electrostatic flux, defined by eqn (2.6), that links the two ions i and j ... 

External fouling is caused by the formation of a cake layer of cells or other materials on the membrane surface, leading to a reduction in permeate flux (defined as the volume of permeate produced per time and membrane area). Internal fouling is caused mainly by proteins and particles smaller than membrane pores. Proteins and protein aggregates can adsorb or deposit at the pore entrance or inside the pores and cause pore blockage or narrowing, leading to increased hydraulic resistance (2). 

The reference time scale r depends on the system to be simulated, as will be seen in the next section, where some model systems are described. There, the characteristic distance 6 will also be defined as used in this book (Sect. 2.4.1). Other variables that are normalised are the current and electrode potential. Current i is proportional to the concentration gradient, by Fick s first equation (2.2), as expressed in (2.9). We introduce the dimensionless gradient or flux, defined as... 

The procedure for numerical integration is as follows. Initial conditions are first selected cA, cB, cAB and from this initial state the concentrations of the three component species are altered stepwise using fluxes defined from the differential equation given above, with a finite time increment At. 

The ratio of the droplet spray flux to the sohds flux defines a dimensionless spray flux given by... 

The diffusion fluxes defined earlier are seen to be special cases of the more general definitions presented above. Table 1.3 summarizes the most commonly encountered diffusion fluxes and Table 1.4 summarizes those fluxes that are measured with respect to a laboratory fixed coordinate reference frame. 

Flux defined in terms of a mass transfer coefficient, k, with an external, known concentration, cq, or a heat transfer coefficient, h, with an external, known temperature, To (called a Robin condition or boundary condition of the third kind) ... 

The boundary condition, eq. (9.32), means that the component fluxes, defined according to the gas- and liquid film properties, must be equal to each other. At the interface chemical equilibrium is usually assumed. The concentration of i in the gas and liquid phases are then related to each other according to... 

We have to understand that if the heat flux defined by Equation 3.5 at the rubber sensor is of interest, because it provides the intensity and shape of the cure exotherm, the other taking place in the air, expressed by Equation 3.6, is characterized by the loss in heat for the cure reaction. From a first approach, based on a logical consideration, this loss in heat affects essentially the values of the enthalpy of cure which is reduced somewhat. The shape of the exotherm, which gives rise to the kinetics of the reaction, should not be affected as in Equation 3.6, the loss in heat is proportional to the difference in temperatures, in the same way as for the gradient of temperature shown in Equation 3.5. The loss in heat could follow kinetics similar to that observed on the sensor of the calorimeter. 

Neutron fluxes, defined as the total track length per unit volume, are calculated in every region of the system in the full energy spectrum, but are finally condensed to 16 energy groups. Reaction rates may also be obtained... 

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