With constant heat transfer

Peaking and Non-isothermal Polymerizations. Biesenberger a (3) have studied the theory of "thermal ignition" applied to chain addition polymerization and worked out computational and experimental cases for batch styrene polymerization with various catalysts. They define thermal ignition as the condition where the reaction temperature increases rapidly with time and the rate of increase in temperature also increases with time (concave upward curve). Their theory, computations, and experiments were for well stirred batch reactors with constant heat transfer coefficients. Their work is of interest for understanding the boundaries of stability for abnormal situations like catalyst mischarge or control malfunctions. In practice, however, the criterion for stability in low conversion... 

Example 5.11 The results of Table 5.1 suggest that scaling a tubular reactor with constant heat transfer per unit volume is possible, even with the further restriction that the temperature driving force be the same in the large and small units. Find the various scaling factors for this form of scaleup for turbulent liquids and apply them to the pilot reactor in Example 5.10. 

Solution Now, Ar=107°C. Scaling with geometric similarity would force the temperature driving force to increase by S = 1.9, as before, but the scaled-up value is now 201°C. The coolant temperature would drop to —39°C, which is technically feasible but undesirable. Scaling with constant pressure forces an even lower coolant temperature. A scaleup with constant heat transfer becomes attractive. 

Determine the reactor length, diameter, Reynolds number, and scaling factor for pressure drop for the scaleup with constant heat transfer in Example 5.12. 

The basis of the method was stated by Silver (1947). A numerical solution of a condenser for mixed hydrocarbons was carried out by Webb and McNaught (in Chisholm, 1980, p. 98) comparison of the Silver-Bell-Ghaly result with a Colburn-Hougen calculation showed close agreement in this case. Bell and Ghaly (1973) claim only that their method predicts values from 0 to 100% over the correct values, always conservative. A solution with constant heat transfer coefficients is made in Example 8.11 A recent review of the subject has been presented by McNaught (in Taborek et al., 1983, p. 35). 

Scaleup with constant heat transfer is theoretically possible with any form of scaleup, provided the wall driving force can be adjusted as shown in Table 10.2. 

For heat exchangers in true counter-current (fluids flowing in opposite directions inside or outside a tube) or true co-current (fluids flowing inside and outside of a tube, parallel to each other in direction), with essentially constant heat capacities of the respective fluids and constant heat transfer coefficients, the log mean temperature difference may be appropriately applied, see Figure 10-33. ... 

It supplies heat, by condensing, at a constant temperature and with high heat transfer coefficients, so it maximizes the effectiveness of heat exchangers ... 

Equation (l) shows the rate of polymerization is controlled by the radical concentration and as described by Equation (2) the rate of generation of free radicals is controlled by the initiation rate. In addition. Equation (3) shows this rate of generation is controlled by the initiator and initiator concentration. Further, the rate of initiation controls the rate of propagation which controls the rate of generation of heat. This combined with the heat transfer controls the reaction temperature and the value of the various reaction rate constants of the kinetic mechanism. Through these events it becomes obvious that the initiator is a prime control variable in the tubular polymerization reaction system. 

Assume convective heating only with a constant heat transfer coefficient, h = 25 W/m2 K. 

The other extreme case is the adiabatic change, which occurs with no heat transfer between the gas and the surroundings. For a reversible adiabatic change, k = y where y = Cp/Cv, the ratio of the specific heat capacities at constant pressure (Cp) and at constant volume (C ). For a reversible adiabatic change of an ideal gas, equation 6.27 becomes... 

In this section, the basic theory required for the analysis and interpretation of adsorption and ion-exchange kinetics in batch systems is presented. For this analysis, we consider the transient adsorption of a single solute from a dilute solution in a constant volume, well-mixed batch system, or equivalently, adsorption of a pure gas. Moreover, uniform spherical particles and isothermal conditions are assumed. Finally, diffusion coefficients are considered to be constant. Heat transfer has not been taken into account in the following analysis, since adsorption and ion exchange are not chemical reactions and occur principally with little evolution or uptake of heat. Furthermore, in environmental applications,... 

When processes are subject only to slow and small perturbations, conventional feedback PID controllers usually are adequate with set points and instrument characteristics fine-tuned in the field. As an example, two modes of control of a heat exchange process are shown in Figure 3.8 where the objective is to maintain constant outlet temperature by exchanging process heat with a heat transfer medium. Part (a) has a feedback controller which goes into action when a deviation from the preset temperature occurs and attempts to restore the set point. Inevitably some oscillation of the outlet temperature will be generated that will persist for some time and may never die down if perturbations of the inlet condition occur often enough. In the operation of the feedforward control of part (b), the flow rate and temperature of the process input are continually signalled to a computer which then finds the flow rate of heat transfer medium required to maintain constant process outlet temperature and adjusts the flow control valve appropriately. Temperature oscillation amplitude and duration will be much less in this mode. 

For material initially undamaged, the appropriate parameter expressing the tendency for cracks to be developed, and therefore strength to be lost, can be considered to be that for crack initiation. This has been expressed in terms of thermal stress resistance parameters.25,30,52,86-88 Kingery used the infinite slab symmetrically heated or cooled with a constant heat transfer coefficient to derive thermal shock fracture resistance parameters R, R and fusing the equations ... 

Example 2.4. Two metal objects Bi and B2 (with constant masses m and m2 and constant heat capacities Cp and Cp2, respectively), initially at different temperatures (Tji0 and T2io), are brought into contact. Heat transfer occurs over a contact area A, with a heat-transfer coefficient U. The objects are assumed to be isolated from the environment however, the insulation on B2 is not perfect and heat is lost to the environment over a similar area A the heat transfer coefficient U, between l>2 and the environment is, however, much lower than U. The environment is assumed to act as a heat sink at a constant temperature Te. 

The feedline is planned in a way that even high melting, high viscous or oxidation sensitive substances can be fed into the column. The feed vessel has a temperature controlled wall and bottom heating. It is equipped with an inert gas pipe to prevent the feedstock from oxidative reactions. A stirrer ensures a constant heat transfer from the walls to the feed bulk... 

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