Tubular geometry

FIGURE 13.10 Electric field as a function of radial distance (tubular geometry). 

The surface shear stress t is a consequence of the velocity difference between the metal surface and the fluid velocity. For tubular geometries it can be obtained from pressure drop measurements or calculated ... 

The zero slope boundary condition at = 0 assumes S5anmetry with respect to the centerline. The mathematics are then entirely analogous to those for the tubular geometries considered previously. Applying the method of lines gives... 

CNTs have received tremendous interest from both fundamental and applied research due to their unique physical properties [39]. These properties stem from their aromatic nature as well as the quasi ID tubular geometry that renders many properties anisotropic. Table 1.1 summarizes the most important properties of CNTs. 

Various types of discharge chambers are available with plate or tubular geometry. The classical and most frequently used type is the tubular, often also called Van der Made-type or Welsbach-type (Figure 2-2). The central rod electrode technology is a more recent development, especially designed for applications with pure oxygen as feed gas (Masschelein, 1994). 

The equations implemented are those defined in Sections 3.2-3.4, i.e. in a partial differential form, for each cell component. This approach is also referred to as Computational Fluid Dynamic (CFD). In order to illustrate the capabilities of the model, in terms of assessment of particular phenomena taking place within the fuel cell, one particular problem is analyzed for each geometry. In particular, for the disk-shaped cell, emphasis is put on the effect of the gas channel configuration on the gas distribution, and, ultimately, on the resulting performance. For the tubular geometry, three different options for the current collector layouts are analyzed. 

The choice of the tubular geometry is related to its main advantages in terms of quick start-up, mechanical resistance, and possibility of realizing sealless stacks. The reduced size drastically reduces thermal shocks and the related mechanical stress, due to quick load changes and start-up/shut-down. 

The choice of the tubular geometry, however, introduces a number of possibilities for the current collector layouts, and different cell performance is expected in each case. Three possibilities are here analyzed ... 

Sanchez, D., Chacartegui, R., Munoz, A. and Sanchez, T. (2006) Thermal and electrochemical model of internal reforming solid oxide fuel cells with tubular geometry, Journal of Power Sources 160(2), 1074-1087. 

Derive the equation that describes the thickness distribution after thermoforming the constant diameter tubular geometry described in Fig. 6.75. Use the notation presented in the figure. Assume that the sheet stops stretching once it touches the mold wall. 

Lead and electrode inductance can be somewhat less in discs than in tubes so that discs have some advantage at higher frequencies. The two shapes are similar in volumetric efficiency since their bulk largely consists of the encapsulating resin. The tubular geometry is suited to the manufacture of feed-through capacitors. A schematic diagram of the cross-section of such a capacitor is shown in Fig. 5.10. These are used as bypass capacitors in television and FM tuners. 

The coefficients / i, / 2, and j03 depend on the flow profile and the local shear rates of the system, and j04 depends on the reactor geometry and for a tubular geometry,... 

They withstand more pressure than other reactors due to the tubular geometry of the flow space. This allows working in the turbulent regime. 

The roughness of the silica surface could introduce the steric hindrance of the surface accessibility similar to the effect of the micropores. In the discussion above, we assume the ideal tubular geometry of the silica surface. The use of different probe molecules for the BET measurement of silica surface area (such as N2, Ar, Kr, benzene, etc.) leads to significant difference in the surface area values for the same silica sample. It was suggested that silica surfaces possess the property of fractals [16] this essentially means that molecules of different size will see a different surface area. 

Adopting the dusty gas model(DGM) for the description of gas phase mass transfer and a Generalized Stefon-Maxwell(GSM) theory to quantify surface diffusion, a combined transport model has been applied. The tubular geometry membrane mass balance is given in equation (1). 

The configuration of the fuel cells is not limited to the tubular geometry. Michaels el al. [1986] fabricated monolithic fuel cells which basically have a crossflow configuration and all unit cells connected in scries (Figure 11.47) or in parallel (Figure 11.48) for the... 

When membranes are produced in a tubular geometry, which seems the most feasible currently, all membranes have to be sealed separately. This favours tubes with large diameters to reduce the number of seals. On the other hand, the smaller the tube diameter, the higher the specific surface area attainable in a module. 

Endothermic reactions, such as steam reforming, are usually carried out in long narrow tubes filled with catalysts and externally heated by flames. The heat could be provided more uniformly and more accurately at the necessary level by a combustion catalyst coated on the outside of the tubes, and heat transfer rates could be further improved by coating the endothermic reaction catalyst on the inner wall of the tube. In this way, the heat of combustion is transferred to the heat sink (the endothermic reaction) through the solid wall, avoiding solid-gas heat transfer resistances. However, the tubular geometry is not most efficient for this application because of the difficulty to coat the inside of the tubes and the need to include static mixers to facilitate mass transfer to the catalytic surfaces. 

Figure 12.18 Example of SOFC geometries, (a) Tubular geometry ofthe Siemens-Westinghouse system (b) Planar structure ofthe Sulzer-Hexis SOFC (for details, see the text).

The analytical forms derived by Dresner (11) for rectangular channels were converted for tubular geometry (, 10). By comparison with exact results obtained by infinite series methods, a semi-empirical form was derived (12) to extend Dresner s analytical result beyond the entrance region. For our experiments the following results are Important ... 

Recently, perylene-3,4,9,10-tetracarboxyl dianhydride (PTCDA) has been reported to be incorporated into an SWNT. The filled nanotube could then be converted into a DWNT by heating to about 1000°C. PTCDA is known to form graphene layers upon heating to 2800 °C. Now given the spatial confinement inside the tube, it is forced to adopt a tubular geometry. 

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