Conductance upstream

The boundary conditions in Problem 11.8 are not really appropriate since there can be conduction upstream into the unheated region. Solve the problem from z= -2 to 6, including the upstream region. Use Pe = 20. The equations are... 

Calculate line conductance upstream of valve using the velocity-head to conductance equation (4.52) ... 

Ignition of the current in the PEM fuel cell requires sufficient water buildup in the membrane to sustain the current to produce more water. When the reactants are fed co-currently the small amount of water produced is continually transported down-stream toward the exits of the flow channels. The water slowly accumulates near the exit until a critical level of water is achieved that results in ignition. After ignition near the exit of the flow channels, the water is conducted upstream by diffusion both through the gas phase and through the membrane. The diffusion of water upstream leads to the propagation of the current ignition toward the inlet of the flow channels. 

Magnetic flow meters are sometimes utilized in corrosive Hquid streams or slurries where a low unrecoverable pressure drop and high rangeabiHty is required. The fluid is required to be electrically conductive. Magnetic flow meters, which use Faraday s law to measure the velocity of the electrically conductive Hquid, are relatively expensive. Their use is therefore reserved for special situations where less expensive meters are not appropriate. Installation recommendations usually specify an upstream straight mn of five pipe diameters, keeping the electrodes in continuous contact with the Hquid. 

The maximum velocity at the axis is twice the average, whereas the velocity at the wall is zero. The effect of the burner wall is to cool the flame locally and decrease the burning velocity of the mixture. This results in flame stabilization. However, if the heat-transfer processes (conduction, convection, and radiation) involved in cooling the flame are somehow impeded, the rate of heat loss is decreased and the local reduction in burning velocity may no longer take place. This could result in upstream propagation of the flame. 

Equation (2-3.7) suggests that at very low values of conductivity (/c 0.01 pS/m), charge will relax extremely slowly from a liquid. Eilters for example would have to be an hour or more upstream of tanks before the charge would dissipate to 5% of its initial value. 

To overcome thermal entry effects, the segments may be virtually stacked with the outlet conditions from one segment that becomes the inlet conditions for the next downstream section. In this approach, axial conduction cannot be included, as there is no mechanism for energy to transport from a downstream section back to an upstream section. Thus, this method is limited to reasonably high flow rates for which axial conduction is negligible compared to the convective flow of enthalpy. At the industrial flow rates simulated, it is a common practice to neglect axial conduction entirely. The objective, however, is not to simulate a longer section of bed, but to provide a developed inlet temperature profile to the test section. 

Fig. 1. Process flow sheet for the continuous conversion of latex in a counterrotating, tangential twin-screw extruder as it might be arranged for the production of acrylonitrile-butadiene-styrene polymer (Nichols and Kheradi, 1982). Polystyrene (or styrene-acrylonitrile) melt is fed upstream of the reactor zone where the coagulation reaction takes place. Washing (countercurrent liquid-liquid extraction) and solids separation are conducted in zones immediately downstream of the reactor zone. The remainii zones are reserved for devolatilization and pumping.

The HIPS resin was extruded at screw speeds of 30, 60, and 90 rpm at barrel temperatures of 200, 220, and 240 °C for Zones 1, 2, and 3, respectively. The screw temperatures in Zone 3 as a function of time at the screw speeds are shown in Fig. 10.20. Because the RTDs were positioned within 1 mm of the screw root surface, they were influenced by the temperature of the material flowing in the channels. Prior to the experiment, the screw was allowed to come to a steady-state temperature without rotation. Next, the screw speed was slowly increased to a speed of 30 rpm. The time for the screw to reach a steady state after changing the screw speed to 30 rpm was found to be about 10 minutes. The temperature of the T12 and T13 locations decreased with the introduction of the resin. This was caused by the flow of cooler solid resin that conducted energy out from the screw and into the solids. At sensor positions downstream from T13, the screw temperature increased at a screw speed of 30 rpm, indicating that the resin was mostly molten in these locations. These data suggest that the solid bed extended to somewhere between 15.3 and 16.5 diameters, that is, between T13 and T14. When the screw speed was increased to 60 rpm, the T12 and T13 sensors decreased in temperature, the T14 sensor was essentially constant, and the T15, T16, and T17 sensor temperatures increased. These data are consistent with solids moving further downstream with the increase in screw speed. For this case, the end of the solids bed was likely just upstream of the T14 sensor. If the solid bed were beyond this location, the T14 temperature would have decreased. Likewise, if the solid bed ended further upstream of the T14 sensor, the temperature would have increased. When the screw speed was increased to 90 rpm, the T12, T13, and T14 temperatures decreased while the T15, T16, and T17 temperatures increased. As before, the solids bed was conveyed further downstream with the increase in screw speed. At a screw speed of 90 rpm, the solid bed likely ended between the T14 and T15 sensor positions, that is, between 16.5 and 17.8 diameters. These RTDs were influenced by the cooler solid material because they were positioned within 1 mm of the screw root surface. 

The creation of eddies in a combustion zone is dependent on the nature of the flow of the unburned gas, i. e., the Reynolds number. If the upstream flow is turbulent, the combustion zone tends to be turbulent. However, since the transport properties, such as viscosity, density, and heat conductivity, are changed by the increased temperature and the force acting on the combustion zone, a laminar upstream flow tends to generate eddies in the combustion zone and here again the flame becomes a turbulent one. Furthermore, in some cases, a turbulent flame accompanied by large-scale eddies that exceed the thickness of the combustion wave is formed. Though the local combustion zone seems to be laminar and one-dimensional in nature, the overall characteristics of the flame are not those of a laminar flame. 

---