NON-ISOTHERMAL

Non-isothermal.—Although rate parameters may have little mechanistic significance, they are at least important in measuring the dwell time in moulds, etc. to optimize the crystallinity and physical properties. In practical situations, the mould is cooled and crystallization occurs under non-isothermal conditions. Jeziorny has used thermal analysis to follow the development of crystallinity in poly(ethylene terephthalate) at different cooling rates. Equation (6) was assumed to be valid for isothermal crystallization, and the temperature dependence of Zi was assumed from Ziabichi s approximation,  

Poisson, Recherches sur la probabilitie des jugements en matiere criminelle et en matiere civile, 

Hendra et ai. have quenched poly(oxymethylene) and polyethylene at various cooling rates quenched in liq. Nj, and from 40 to 320 K min and different melt temperatures, 650 to 430 K, and observed that the lamellae thickness varied markedly with both parameters. Since the random coil dimensions are temperature dependent, they suggest that the crystallized material retains a memory of the melt random coil dimensions. Similarly, hydrostatic pressure applied to the melt also reduced the lamellae thickness. The authors have dismissed the effect of heat losses on crystallization as irrelevant. 

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Navler-Stokes equation, 26 Non-isothermal catalyst pellet, 156-... 

In this chapter the general equations of laminar, non-Newtonian, non-isothermal, incompressible flow, commonly used to model polymer processing operations, are presented. Throughout this chapter, for the simplicity of presentation, vector notations are used and all of the equations are given in a fixed (stationary or Eulerian) coordinate system. 

The theoretical description of a non-isothermal viscoelastic flow presents a conceptual difficulty. To give a brief explanation of this problem we note that in a non-isothennal flow field the evolution of stresses will be affected by the... 

As already mentioned, the present code corresponds to the solution of steady-state non-isothennal Navier-Stokes equations in two-dimensional Cartesian domains by the continuous penalty method. As an example, we consider modifications required to extend the program to the solution of creeping (Stokes) non-isothermal flow in axisymmetric domains ... 

Figure 1.6.1 Comparison of asymptotic and exact solutions for a first order, non-isothermal reaction in a spherical catalyst pellet. ...

Because of this heat generation, when adsorption takes place in a fixed bed with a gas phase flowing through the bed, the adsorption becomes a non-isothermal, non-adiabatic, non-equilibrium time and position dependent process. The following set of equations defines the mass and energy balances for this dynamic adsorption system [30,31] ... 

Guilleminot, J.J., Meunier, F. and Paklc2a, J., Heat and mass transfer in a non-isothermal fixed bed solid adsorbent reactor a uniform-pressure non-uniform temperature case. International Journal of Heat and Mass Transfer, 1987, 30(8), 1595 1606. 

Sampling of a two-fluid phase system containing powdered catalyst can be problematic and should be considered in the reactor design. In the case of complex reacting systems with multiple reaction paths, it is important that isothermal data are obtained. Also, different activation energies for the various reaction paths will make it difficult to evaluate the rate constants from non-isothermal data. 

Equation 5-16 is the time required to aehieve a eonversion Xa for either isothermal or non-isothermal operation. Equation 5-16 ean also be expressed in terms of eoneentration at eonstant fluid density as... 

Most chemical reactions are greatly affected by temperature. The previous chapters discussed reactions at isothermal condition, however, industrial reactors often operate under non-isothermal condition. This is because chemical reactions strongly depend on temperature, either absorbing (i.e., endothermic) or generating (i.e., exothermic) a large amount of heat. 

Consider a non-isothermal bateh reaetor that is operated adiabatieally. The reaetor eontains a liquid reaetion mixture in whieh the reaetion A —> Produets oeeurs, where (-r ) = kC and k = kge , ... 

Figure 6-5b Temperature versus time in an adiabatic batch reactor. Fig ure 6-5. Simulation of a non-isothermal batch reactor.

Simulation of a non-isothermal reaction in a batch reactor involving the hydrolysis of acetylated castor oil... 

The various types of reaetors employed in the proeessing of fluids in the ehemieal proeess industries (CPI) were reviewed in Chapter 4. Design equations were also derived (Chapters 5 and 6) for ideal reaetors, namely the eontinuous flow stirred tank reaetor (CFSTR), bateh, and plug flow under isothermal and non-isothermal eonditions, whieh established equilibrium eonversions for reversible reaetions and optimum temperature progressions of industrial reaetions. 

Equation 7-101 ean also he used to ealeulate the heat-up time for non-isothermal heating (e.g., hy hot-water jaeketing), provided that the differenee between the outlet and inlet jaeket temperatures is not greater than 10% of the differenee between the hateh and average water temperature [47]. 

The non-isothermal heating medium has a eonstant flowrate Wj, speeifie heat Cj, and inlet temperature Tj, but a variable outlet temperature. Eor an unsteady state operation ... 

When cooling a batch with internal coil and a non-isothermal cooling medium, the following equation can be applied. 

Table 7-19 gives the eomputer results from the software (BATCH) for bateh eooling, non-isothermal eooling medium. 

BATCH COOLING EXTERNAL HEAT EXCHANGER (COUNTER-CURRENT FLOW), NON-ISOTHERMAL COOLING MEDIUM... 

Table 7-20 shows the computer results using an external heat exchanger involving a non-isothermal cooling medium. 

BATCH HEATING EXTERNAL HEAT EXCHANGER AND NON-ISOTHERMAL HEATING MEDIUM... 

When heating a batch reactor with an external heat exchanger and non-isothermal heating, the following equation applies ... 

Batch heating/cooling of fluids external heat exchanger (counter-current flow) non-isothermal cooling medium... 

In predicting the time required to cool or heat a process fluid in a full-scale batch reactor for unsteady state heat transfer, consider a batch reactor (Figure 13-2) with an external half-pipe coil jacket and non-isothermal cooling medium (see Chapter 7). From the derivation, the time 6 to heat the batch system is ... 

Alternatively, for bateh heating with a non-isothermal heating medium, the log mean temperature differenee AUj p is determined by... 

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