Non-isothermal effect

The last factor reflects the role of the non-isothermal effect on the kinetics of the process. The complete kinetic equation for non-isothermal polymerization can be written as... 

Eq. (2.85) is also applicable in this case, but the dimensionless shear rate must be replaced with another dimensionless parameter 5, which characterizes the non-isothermal effect. This is expressed as... 

There are three main sources of non-isothermal effects which can play different roles in real processes ... 

Injection molding is a rather complex process during which non-Newtonian as well as non-isothermal effects play significant roles. Here, we present a couple of problems that are relatively simple to allow an analytical solution. Injection molding is discussed further in the next chapters. 

Although we analyze most polymer processes as isothermal problems, many are non-isothermal even at steady state conditions. The non-isothermal effects during flow are often difficult to analyze, and make analytical solutions cumbersome or, in many cases impossible. The non-isothermal behavior is complicated further when the energy equation and the momentum balance are fully coupled. This occurs when viscous dissipation is sufficiently high to raise the temperature enough to affect the viscosity of the melt. 

Fig. 11.6 Dimensionless heat generation rates for various values of the dimensionless activation energy. [Reprinted by permission from D. H. Sebastian, Non-Isothermal Effects in Polymer Reaction Engineering, in Temperature Control Principles for Process Engineers, E. P. Dougherty, Ed., Hanser, Munich, 1993.]...

Although these chemical analyses of propane oxidation [13] are among the best that have been reported, it is rather difficult to make a clear judgement from them on the applicability of the alkylperoxy radical mechanism of oxidation. There is reasonable evidence in support of enhanced yields of propene at higher temperatures, especially if allowance is made for the non-isothermal effects in cool-flames. The susceptibility of... 

The isothermal and non-isothermal effectiveness factors for the single unimolecular irreversible reaction. Equilibrium adsorption-desorption model with linear isotherm For simplicity of presentation and without any loss of generality we consider here the case where the bulk temperature and concentration are taken as the reference temperature and concentration. In this case the boundary conditions (5.127) become at fu= 1.0... 

Non-isothermal ejfectiveness factor The non-isothermal effectiveness factor can be obtained numerically only by integrating the two points boundary value differential equations using different numerical techniques, the most efficient of these techniques is the orthogonal collocation method. 

For a spherical particle the non-isothermal effectiveness factor t] is defined as ... 

FIGURE 5.49 Intraphase non-isothermal effectiveness factor versus 70 for linear kinetics y = 20, Sh, Nu = oo. 

Fig. 15. Non-isothermal effectiveness factor for spherical particle as function of the Thiele modulus, . Adapted from Weisz and Hicks (1962) and Trambouze et al. (1988).

Concerning the DECOVALEX benchmarks our part of the work is restricted to isothermal conditions. Multiphase flow modeling considering non-isothermal effects is performed by the Center for Applied Geosciences (2 G) in Tubingen, Germany. 

In the future, the presented coupling strategy will incorporate ongoing developments within the RockFlow code concerning non-isothermal effects in multiphase (liquid/gas) flow modeling, De Jonge, Kolditz (ZAG). 

Non-isothermal effects, due to sudden increase in catalyst temperature... 

Garside, J. and Tavare, N.S. (1981) Non-isothermal effectiveness factors for crystal growth. Chemical Engineering Science, 36, 863-866. 

Values of k[ at a particular temperature and pressure are determined by measuring how [7] changes with time using infrared spectroscopy or other techniques. The experimental difficulty increases as half-life shortens, as special care must be taken to eliminate transient non-isothermal effects. Decomposition kinetics are summarized for a wide range of initiators in reference 5 and in trade literature available from commercial suppliers. Of special note is the work of Buback et al. [7, 8] that systematically examines how Ej and A Vi vary with alkyl substituent for the peroxyester family, and how the substituent choice affects the decomposition pathway and initiator efficiency. 

The N2O decomposition reaction is especially interesting because under particular conditions the reaction can be induced to oscillate (see Fig. 4.28l l). If non-isothermal effects can be excluded, this implies the presence of an auto-catalytic elementary reaction step in the overall catalytic reaction cycle (see Chapter 8). In this case, the auto-catalysis results from N2O decomposition catalyzed by both mono-center and bi-center iron complexes. 

Tavera EM. Analytical expression for the non-isothermal effectiveness factor The nth-order reaction in a slab geometry. Chemical Engineering Science 2005 60 907-916. 

Hoyos B, Cadavid JG, Rangel H. Formulation and numerical calculation of non-isothermal effectiveness factor for finite cylindrical catalysts with bidimensional diffusion. Lat. Am. Appl. Res. 2004 34 17. 

Non isothermal phenom ia are present to scane extent in all gas absorption operations. As se i above the importance of the non isothermal effects arises from their influence on the mass transfer rate and, in the case of chemical absorption, from their influence on reaction rates and selectivities. This means that to neglect the boundary condition coiq>ling between solubility and interface temperature may lead to serious overestimates of the absorption rates and to model the non isothermal absorption process, it is necessary to consider the mass and energy balance equations simultaneously. Attention has been ccmsiderably focused both experimentally and theoretically on that important topic particularly during these 3 or 4 last years (14 -. ... 

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