Integrated channel cross sections

Transferring Eq. (4.15) to divergent form and integrating this equation through the micro-channel cross-section we obtain ... 

Using the above definitions and integrating over the channel cross section, with some manipulations, Zuber s kinematic equation results (Hsu and Graham, 1976) ... 

Results of numerical integration of Eq. (29) are represented in Fig. 5. For ordinary flames a 0.1-0.2 the flame propagation velocity along the channel is greater than the normal flame velocity by a factor of 1.25-1.40. The stagnation zone in the combustion products occupies about a quarter of the channel cross section. 

For most small systems the chemical and electronic channels are rather obvious and therefore the labels 7 and e will be omitted hereafter. Normally, one measures integral absorption cross sections,... 

Integration over the channel cross-sectional area yields the average velocities ... 

The figure 4 shows that for large values of Z high velocity gradient appears near die wall surface R=l. Integration over die channel cross-sectional area yields the average velocities ... 

Now, the optimal size is evidently such that the particles are displaced across the channel by the two independent deposition processes in the same time. Approximately (without integrating over the channel cross section), the condition can be written like... 

Fig. 10. Integral reaction cross sections for H + H2, with reactants and products in their ground vibrational states. Results are from coupled-channel (WK.) calculations (Wolken and Karplus, 1973) and = 0 - jb = 1 from two-state (McM) calculations (McGuire and Micha, 1973) and from distorted-wave (TK) calculations (Tang and Karplus, 1971). The last two for...

An experimental setup detecting the formed target ions Cs+ or Cs after the collision with clusters could provide pure ct cross sections, i.e. without regard to the evolution of the cluster. The calculated integral ct cross sections cluster size n in Fig. 5. Note that the ground state Cs (6s21S ) is expected to be bound [36]. Obviously, the cross sections for the normal ct process with Cs+ in the exit channel are considerably larger (at least a factor of two) than for the exotic Cs- formation, and the size dependences show... 

The size dependence of a+ exhibits a strong similarity to that of the exclusive ct cross section an for channel (15), which holds for T = 0 as well as for liquid projectile clusters. The absolute values of cr+, however, are considerably larger than those of a , because the fragmentation channels deplete the integral ct cross section. 

For successful application of carbon-coated monolithic catalysts, the deposition of active phase in the walls of a monolithic substrate should be prevented. To prevent deposition of ruthenium in the wall (1) substrates with nonporous walls can be used, or (2) the cordierite monolithic substrates can be modified with a-AEOs, blocking the macroporosity of the cordierite and rounding the channel cross section to enable a more uniform thickness of the carbon coating layer. Alternatively, ACM monoliths or integral carbon monoliths with very thin walls having a characteristic diffusion length similar to the activated carbon slurry catalysts can be employed. 

Consider an excitation function a v) of an ion-molecule reaction for which, in order to simplify the discussion, any consideration of internal energy may be ignored. This can be included (and must be for any real system). It complicates the situation and some indication of this is given in the footnotes accompanying the following discussion. The excitation function, which summarizes the energy dependence of the integral reactive cross section for the particular reactive channel under consideration, is the fundamental measure of the total reaction efficiency for that... 

Time-of-flight (TOF) measurement is popular in microflow measurements. The time of flow of a pulse of temperature or of molecular tracers from one point in a microchannel to another point is characterized to measure the flow rate. An emitter and a collector are integrated into TOF sensors. Various optimizations of these sensors have been carried out, using temperature pulses or electrochemical production of molecular tracers. These sensors calculate the flow rate at one point in the cross section of the channel and are calibrated with a known flow rate. Flow measurementusing microparticles captures the velocity profile at many such locations in the channel cross section and allows one to calculate the flow rate. Figure 4 shows the principle of a flow sensor using a CFD simulation of convective diffusion... 

The integration over the channel cross section of Eqs. 1 and 2 allows the calculation of the axial distribution of the fluid bulk temperature locally defined as follows ... 

Let us consider the heated microchannel subjected to the HI boundary condition. By integrating Eq. 2 over the channel cross-sectional area f2, one obtains the following result ... 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

Integration of Eqs. (4.28) and (4.29) through the cross-section of the micro-channel gives ... 

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