External heat transferred

In the ease of exothermie or endothermie reaetions, seale-up may impair eonditions for heat input or removal beeause the ratio of the heat transfer surfaee area to the reaetor volume is redueed. Identieal eonditions for heat transfer in both the model and full-seale plants may be aehieved in exothermal reaetions if both have the same thermal stability eoeffieient. This requirement is obtained by introdueing external heat exehangers. Alternatively, a reaetor with a strong exothermie reaetion ean be divided into several small size reaetors. In this manner, the ratio of the external heat transfer surfaee area to the reaetor volume is inereased, thereby avoiding an exeessive temperature rise in the reaetor. 

Thermal difl usiviiy of the surrounding fluid Du =2 x 10 nr/s External heat transfer coefficient h =100 W/rrrK... 

The existence of three steady states, two stable and one metastable, is common for exothermic reactions in stirred tanks. Also common is the existence of only one steady state. For the styrene polymerization example, three steady states exist for a limited range of the process variables. For example, if Ti is sufficiently low, no reaction occurs, and only the lower steady state is possible. If Tin is sufficiently high, only the upper, runaway condition can be realized. The external heat transfer term, UAextiTout — Text in Equation (5.28) can also be used to vary the location and number of steady states. 

Example 5.8 Suppose that, to achieve a desired molecular weight, the styrene polymerization must be conducted at 413 K. Use external heat transfer to achieve this temperature as the single steady state in a stirred tank. 

GP 11] [R 19] For an autothermal reactor, i.e. a device with neither internal nor external heat transfer, steep temperature profiles along the flow axis were found [9]. Via an inspection window, glowing of the front zone of the wire reactor was observed, indicating complete conversion within a few mm reaction passages. The... 

The power versus efficiency characteristics of the endoreversible Carnot heat engine is a parabolic curve. The endoreversible heat engine is a simple model, which considers the external heat-transfer irreversibility between the heat engine and its surrounding heat reservoirs only. 

Figure 17.9. Stirred tank reactors, batch and continuous, (a) With agitator and internal heat transfer surface, batch or continuous, (b) With pumparound mixing and external heat transfer surface, batch or continuous, (c) Three-stage continuous stirred tank reactor battery, (d) Three-stage continuous stirred tank battery in a single shell.

Figure 17.18. Heat transfer in fixed-bed reactors (a) adequate preheat (b) internal heat exchanger (c) annular cooling spaces (d) packed tubes (e) packed shell (f) tube and thimble (g) external heat exchanger (h) multiple shell, with external heat transfer (Walas, 1959).

The last boundary condition accounts for the external heat transfer from the adsorbent mass, h is the effective external heat transfer coefficient, a, b, c, p, q, kfi, kg and h can be assumed to be constants for a differential test. 

Equations (19) and (20) correspond to the familiar case of uptake controlled by external heat transfer resistance derived earlier by King and Cassie [25]. Equation (20) shows that (T -T ) is the maximum temperature rise in the adsorbent for this case, and it occurs at t = 0. 

The external heat transfer can be independently controlled, and hence, will not be addressed here. Heat transfer through the solid is given by the following expression ... 

For example, scaling up from 30 to 100m3 reduces the S/V from 1.5 to 1. The effective heat-transfer area depends on the shape factor H/D, which in turn is determined by the technology of the mixing device. As rule of thumb, a reactor of 100 m3 has an external heat-transfer surface of about 100 m2 [1]. 

Criterion Biot determines the ratio of intensity of external heat exchange processes (numerator) and effective thermal conductivity of a hydride layer (denominator). To carry out frontal chemical reactions of hydrogen sorption -desorption, small numbers Biot (Bi<0.1) are preferable. Number Bi can be decreased by several ways 1) decreasing of the characteristic layer size 2) decreasing of intensity of an external heat transfer (but time of non-stationary processes is growing) 3) increasing of effective hydride bed thermal conductivity. 

Heat may be transferred directly as in the burning of solid fuel mixed with the particulates in the sintering of ores or indirectly as in the combustion of fuel to produce hot gases in pellet hardening. External heat transfer may also take place across a metallic surface as in drum and belt driers and flakers. 

The Biot number Bib for heat transport. Analogous to Bim, this is defined as the ration of the internal to external heat transfer resistance (intraparticle heat conduction versus interphase heat transfer). 

So far it has been assumed that both reactions are first order and the pellet can be treated as isothermal. It may be obvious to note that under nonisothermal conditions the ratio of the intrinsic activation energies and, if necessary, the ratio of the external heat transfer coefficients will also affect the apparent selectivity of the catalyst. In addition, if the kinetic orders of the two reactions are different, this will also influence selectivity. 

Analogously to mass transfer, the following equation is used for external heat transfer ... 

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