Planar flow, worked example

Problem 1.3 (Worked Example) Consider a planar flow with the following velocity gradient tensor in the x y plane ... 

Worked example [using the data fi om Hermia 1993], reproduced below, calculate the pressure as a function of time needed to maintain a constant flow rate of 1 m mT h on candle fibers of radii 15 and 10 mm, and for a filter of planar geometry. Data pressure at end of precoating 0.1 bar, beer viscosity 0.003 Pa s, body feed dosage 1 kg mT precoat dosage 1.5 kg specific resistance lxlo m kg and filter aid bulk density 350 kg m.-. The maximum pressure available fi om the pmq> is 3.5 bar. Applying Equation (6.9) at various times provides the results tabulated in Table 6.4. 

Recent mathematical work suggests that—especially for nonlinear phenomena—certain geometric properties can be as important as accuracy and (linear) stability. It has long been known that the flows of Hamiltonian systems posess invariants and symmetries which describe the behavior of groups of nearby trajectories. Consider, for example, a two-dimensional Hamiltonian system such as the planar pendulum H = — cos(g)) or the... 

The beginnings of the SOFC are recorded in an early East German University patent (Mobius and Roland, 1968) which shows awareness of many of the variables still being worked upon today. The oxides of lanthanum, zirconium, yttrium, samarium, europium, terbium, ytterbium, cerium and calcium are mentioned as candidate electrolyte materials. The proposed monolithic planar arrangement has, however, been abandoned by many companies, on the example of Allied Signal. One notable exception is a reversion to a circular planar concept by Ceramic Fuel Cells of Australia, UK (Section 4.7). The Rolls-Royce all-ceramic fuel cell (Section 4.3), which is monolithic and has one compliant feature, namely a gap, is a major exception. One modern trend is towards lower SOFC temperatures, with the intermediate-temperature IT/SOFC allowing the use of cell and stack arrangements with some flexibility and manoeuvrability based on new electrolytes, metallic flow plates, electrodes and interconnects. 

At large values of the ZePdovich number, the chemical reaction is confined to a thin sheet in the flow. For all purposes except the analysis of the sheet structure, the sheet may be treated as a surface—for example, G(x, t) 0—which in terms of the Cartesian coordinates (x, y, z) may be written locally as x = F(y, z, t) if the x coordinate is not parallel to the sheet in its local orientation. When analyses are pursued in outer-scale variables, it is convenient to work in a coordinate system that moves with the sheet. For the undisturbed flow, let the x coordinate be normal to the planar flame,... 

---