Temperature differences external, calculation

We would be remiss if we did not indicate that a significant temperature difference also exists between the bulk fluid and the external surface. This AT has a far greater effect on the observed rate than does the S02 concentration difference. Illustration 12.6 indicates how the temperature difference may be calculated. 

Example 10-1 Experimental, global rates are given in Table 10-2 for two levels of conversion of SOj to SO3. Evaluate the concentration difference for SO2 between bulk gas and pellet surface and comment on the significance of external diffusion. Neglect possible temperature differences. The reactor consists of a fixed bed of x -in. cylindrical pellets through which the gases passed at a superficial mass velocity of 147 lb/(hr)(ft ) and at a pressure of 790 mm Hg. The temperature of the catalyst pellets was 480°C, and the bulk mixture contained 6.42 mole % SOj and 93.58 mole % air. To simplify the calculations compute physical properties on the basis of the reaction mixture being air. The external area of the catalyst pellets is 5.12 ft /lb material. The platinum covers only the external surface and a very small section of the pores of the alumina carrier, so that internal diffusion need not be considered. 

Thus the mass-transfer rate between particle and fluid for a fluidized bed is approximately two orders of magnitude greater than for a fixed bed. With this large transport rate, it is evident that Q — Q, calculated by the methods described in Sec. 10-3, will be negligible. A similar result applies for external temperature differences. 

The reactor consisted of a fixed bed of x --in. cylindrical pellets. The pressure was 790 mm Hg. The external area of catalyst particles was 5.12 ft /lb, and the platinum did not penetrate into the interior of the alumina particles. Calculate the partial-pressure difference between the bulk-gas phase and the surface of the catalyst for SOj at each mass velocity. What conclusions may be stated with regard to the importance of external diffusion Neglect temperature differences. 

For use in reactor design the global rate should be calculable at all locations in the reactor. We suppose that the intrinsic rate equation is available. The problem is to evaluate the global rate corresponding to possible bulk concentrations Q, bulk temperatures 7, and flow conditions. If external and internal temperature differences can be neglected, the problem is straightforward and is essentially the reverse of the stepwise solution outlined in Sec. 12-1. The double-trial procedure is not necessary, because /(C) is known. The effective diffusivity of the catalyst pellet is required. The equations we need are Eq. (10-1) for external diffusion,... 

Fig. 3. Variations of the methyl pentane diffusivity coefficient at room temperature versus the AN ratio for different crystal sizes ofMFI sanities. A corresponds to the external surface of the crystdlites and 7 to their volume (from ref 46). Measurements were made by measuring weight gain rate m by gravimetry at room temperature, k is calculated with the relationship (m /m o) = (ANl /iffl t = k t, D being the diffusion coefficient.

To evaluate the potential of carbon formation in a steam reformer, it is therefore essential to have a rigorous computer model, which contains kinetic models for the process side (reactor), as well as heat transfer models for the combustion side (furnace). The process and combustion models must be coupled together to accurately calculate the process composition, pressure, and temperature profiles, which result from the complex interaction between reaction kinetics and heat transfer. There may also be a temperature difference between bulk fluid, catalyst surface, and catalyst interior. Lee and Luss (7) have derived formulas for this temperature difference in terms of directly observable quantities The Weisz modulus and the effective Sherwood and Nusselt numbers based on external values (8). 

The structural solution computes the full 3D elastic-plastic deformation and stress fields for the solid components of the stack. The primary stress-generation mechanism in the SOFC is thermal strain, which is calculated using the coefficient of thermal expansion (CTE) and the local temperature difference from the material s stress-free temperature. These thermal strains and mismatches in thermal strains between different joined materials cause the components to deform and generate stresses. In addition to the thermal load, the stack will have boundary conditions simulating the mechanical constraints from the rest of the system and may also have external mechanical preloading. The stress solution is obtained based on the imposed mechanical constraints and the predicted thermal field. Figure 26.6 shows... 

The pressure balance is given by Equation (10.2). In the energy balance, the external heat input term is g = UaAT, where U is the overall heat transfer coefficient between the jacket and the reactor, a is the ratio of the heat transfer area and the reactor volume, and AT is the temperature difference between the jacket and the reactor at a length z. The overall coefficient, U, is constructed from the individual coefficients and the resistance of the tube wall. The overall heat transfer coefficient is calculated by the following equation (McCabe etal., 2001) ... 

The torque-vectoring system has the task of applying different torques to the rear axle to reduce the risk of under-steering and to increase agility while cornering. For this purpose, the technical system architecture is realized with the three main modules torque handling, torque position calculation and position control. In order to perform its functionality, the three modules together read several data sources, either sensor, e.g., the disk temperature, or external units, e.g., the nominal torque value, realize a set of computations and finally operate the actuators to distribute the calculated torque to both wheels of the rear axle. 

In many cases, it is necessary to estimate the rate at which a heterogeneous catalytic reaction wfll proceed, if it is controlled by external mass transfer. Alternatively, it may be necessary to estimate the concentration difference (Ca,b — Ca ) and the temperature difference (7b — T ) that are required to sustain a known or measured rate of reaction. Calculations of Ca3 — Ca,s and Tb — Tg are the only way to evaluate the influence of external transport when definitive diagnostic experiments are not feasible. Calculations such as these can be performed using Eqns. (9-38) and (9-40), provided that the transport coefficients kc and h are known, or can be obtained from correlations. 

M is controlled solely by the temperature difference between the cover plates or by the type of scoops employed. If L is the throughput (feed) of the centrifuge, then the requirement that the external flow exert a negligible influence on the internal circulation is equivalent to requiring that the reflux ratio LjM be much smaller than unity. Berman 23) and Ouwerkerk and Los 24) have included the effect of nonnegligible feed rate in the centrifuge calculations. The net result is a reduction in separative power. 

Airflows are determined basically by a steady-state calculation for each time step. At each time step, first, pressures at external nodes are calculated on the basis of the wind pressure coefficients and the actual wind speed and direction. Then, for all conductances, the local pressures at each side of the link are calculated. At internal links, this pressure is dependent on the (unknown) zone pressure p and the aerostatic pressure variation due to the height of the link with respect to the zone reference height. At external links, this pressure is dependent on the external node pressure and the aerostatic pressure variation due to the height of the link with respect to the stack reference height. For the aerostatic pressure, the air density is determined considering the temperature, the humidity, and (if relevant) the contaminant concentrations in the zone or in the outside air, respectively. From this, the pressure differences across each conductance can be calculated, and from this the mass airflow tor each conductance /. 

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