Through-Plane Shapes

This section derives a more general analytical solution to the system of Equations 4.53 through 4.55 (Kulikovsky, 2012a). This solution corresponds to the mixed case of arbitrary proton transport and weak oxygen transport limitations, and is of particular interest, since the CCL in PEFCs usually works in this regime. 

It is convenient to eliminate the overpotential from Equations 4.53 through 4.55. Differentiating Equation 4.53 over x and using the identity cosh - sinh = 1, one arrives at 

In this equation, a reasonable estimate for the derivative under the square root is 9y/9jc 7o- With c 1, the second term under the square root in Equation 4.155 is much greater than unity if jo 1/e. In a PEFC cathode, e 10 -10 (Table 5.7)  

Neglecting unity under the square root in Equation 4.155 leads to 

Note that in Equation 4.156, a negative value of the square root has been taken, as the positive value results in an unphysical solution. 

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FIGURE 4.2 A schematic of a generic catalyst layer. The through-plane shapes of the ionic current density j, the electron current density y e, the feed molecules concentration c, and the local overpotential jj. 

It will be assumed here that the flow enters the duct through a shaped unheated inlet section and that the velocity and temperature are therefore uniform across the inlet plane as illustrated in Fig. 7.12. 

The through-plane thermal conductivity (TC) of a 3.2-mm thick, 5.1-cm diameter disc-shaped test specimen was measmed at 801C using a Holometrix Model TCA-300 Thermal Conductivity Analyzer, which uses ASTM F433... 

Since faults are zones of inherent weakness they may be reactivated over geologic time. Usually, faulting occurs well after the sediments have been deposited. An exception to this is a growth feu/f (also termed a syn-sedimentary fault), shown in Figure 5.7. They are extensional structures and can frequently be observed on seismic sections through deltaic sequences. The fault plane is curved and in a three dimensional view has the shape of a spoon. This type of plane is called listric. Growth faults can be visualised as submarine landslides caused by rapid deposition of large quantities of water-saturated... 

When both solids and gases pass through the distributor, such as in catalytic-cracldng units, a number of variations are or have been used, such as concentric rings in the same plane, with the annuli open (Fig. 17-9a) concentric rings in the form of a cone (Fig. 17-9b) grids of T bars or other structural shapes (Fig. 17-9c) flat metal perforated plates supported or reinforced with structural members (Fig. 17-9d) dished and perforated plates concave both upward and downward (Fig. 17-9e and f). The last two forms are generally more economical. 

Configurations of interest are those using disk-shaped samples cut from crystals in orientations that permit plane waves of uniaxial strain to propagate through their thickness when a uniform load is applied to their face. When the diameter of the disk is sufficiently large in comparison to its thick-... 

A four-ounce Alnico permanent magnet was mounted in a brass yoke. Two wedge-shaped pole pieces of soft iron, each with a slot sawed part way through it, were also attached, and the dumbbell assembly was inserted with the ends of the silica fiber in the slots and the spheres of the dumbbell between the pole pieces, one sphere being a little in front and the other a little behind the plane of the pole pieces, as shown in Figure 1. 

The quantum number / — 1 corresponds to a p orbital. A p electron can have any of three values for Jitt/, so for each value of tt there are three different p orbitals. The p orbitals, which are not spherical, can be shown in various ways. The most convenient representation shows the three orbitals with identical shapes but pointing in three different directions. Figure 7-22 shows electron contour drawings of the 2p orbitals. Each p orbital has high electron density in one particular direction, perpendicular to the other two orbitals, with the nucleus at the center of the system. The three different orbitals can be represented so that each has its electron density concentrated on both sides of the nucleus along a preferred axis. We can write subscripts on the orbitals to distinguish the three distinct orientations Px, Py, and Pz Each p orbital also has a nodal plane that passes through the nucleus. The nodal plane for the p orbital is the J z plane, for the Py orbital the nodal plane is the X Z plane, and for the Pz orbital it is the Jt plane. 

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