Nonisothermal curves

For nitrogen on 4A, Figure 1, the nonisothermal rate data despite the heating could be represented reasonably by usual isothermal Ficks law equations (I), if D/R is taken as 7.5 X 10" min" Thus, the value of D/R calculated from the isothermal equation was 50% larger than that used to derive the nonisothermal curve in Figure 1. Here the temperature maximum occurs at low amounts adsorbed, and the increased rate owing to increased diffusivities is nearly compensated by the decreased equilibrium adsorption at the observed temperatures. Propane... 

Fig. 2 Experimental uptake curves for CO2 in 4A zeolite crystals showing near isothermal behavior in large (34 and 21.5 Jim) crystals (D 9 x 10 cm s at 371 K and 5.2 X 10 cm s at 323 K). The solid lines are the theoretical curves for isothermal diffusion from Eq. 2 with the appropriate value of Ddr. The uptake curves for the small (7.3 jim) crystals show considerable deviation from the isothermal curves but conform well to the theoretical nonisothermal curves with the values of Dc estimated from the data for the large crystals, the value of p calculated from the equilibrium data, and the value of a estimated using heat transfer parameters estimated from uptake rate measurements with a similar system under conditions of complete heat-transfer control. The limiting isothermal curve is also shown by a continuous line with no points. From Ruthven et al. [8]...

It should be noted that unlike the isothermal kinetic curves in Fig. 3.23, the shape of nonisothermal curves does not provide any clear indication of the type of the reaction model. In nonisothermal runs the temperature increases, causing the reaction rate to continuously accelerate. As a result, under nonisothermal conditions all processes exhibit kinetic curves of a sigmoidal shape. 

The chief cases that are the subject of the problems here are zero, first and second order in spheres, slabs and cylinders with sealed flat ends, problems P7.03.03 to P7.03.ll. A summary of calculations of effectiveness is in P7.03.02. The correlations are expressed graphically and either analytically or as empirical curve fits for convenience of use with calculator or computer. A few other cases are touched on L-H type rate equation, conical pores and changes in volume. Nonisothermal reactions are in another section. 

With the development of modern computation techniques, more and more numerical simulations occur in the literature to predict the velocity profiles, pressure distribution, and the temperature distribution inside the extruder. Rotem and Shinnar [31] obtained numerical solutions for one-dimensional isothermal power law fluid flows. Griffith [25], Zamodits and Pearson [32], and Fenner [26] derived numerical solutions for two-dimensional fully developed, nonisothermal, and non-Newtonian flow in an infinitely wide rectangular screw channel. Karwe and Jaluria [33] completed a numerical solution for non-Newtonian fluids in a curved channel. The characteristic curves of the screw and residence time distributions were obtained. 

Figure 18.8 Nonisothermal effectiveness factor curve for temperature variation within the particle. Adapted from Bischoff (1967).

Let us return to the graphical construction we developed in earlier chapters for isothermal reactors, because for nonisothermal reactors T is stiU the area under curves of plots of 1/r versus Cao — CA. For the first-order irreversible reaction in an adiabatic reactor 1/fad is given by... 

Thus we see that for nonisothermal reactors this 1/r versus Cao Ca curve is not always an increasing function of conversion as it was for isothermal reactors even with positive-order kinetics. Since the 1/r curve can have a rninimum for the nonisothermal reactor, we confirm the possibility that the CSTR requires a smaller volume than the PFTR for positive-order kinetics. This is hue even before the multiple steady-state possibilities are accounted for, which we will discuss in the next chapter. This is evident from our 1 /r plot for the PFTR and CSTR and will occur whenever r has a sufficiently large maximum that the area under the rectangle is less than the area under the curve of 1/r versus Cao Ca-... 

Sketch some possible r and 1/r versus Cao curves for an irreversible exothermic reaction for nonisothermal operation. Show that a CSTR becomes even more attractive for nonisothennal operation. 

The principal goal of TSC trap level spectroscopy is to experimentally determine, by comparison of model glow curve with measured ones, the characteristic parameters that govern the nonisothermal relaxation kinetics of the solid. 

For most experiments on nonisothermal TSR, simple cooling of the sample to the desired initial temperature and a linear increase in T after excitation are sufficient to obtain TSC and TSL glow curves. Some techniques require more elaborate heating cycles, the details of which depend on the relaxation mechanism under study and on whether it is necessary to discriminate between simnltaneously occurring processes, e.g., thermally stimulated depolarization and thermally stimulated conductivity (see Chapter 2). 

Equation (3.17) allows a different interpretation of the underlying system s bifurcation behavior by taking Kc and yc as fixed and letting a vary, for example. We now study the bifurcation behavior of nonadiabatic and nonisothermal CSTR systems via their level-zero curves for the associated transcendental surface z = g(a,y). The surface is defined as before, except that here we treat Kc and yc as constants and vary a and y in the 3D surface equation... 

Nonadiabatic, nonisothermal CSTR bifurcation curve for a Figure 3.18... 

Distributed Parameter Models Both non-Newtonian and shear-thinning properties of polymeric melts in particular, as well as the nonisothermal nature of the flow, significantly affect the melt extmsion process. Moreover, the non-Newtonian and nonisothermal effects interact and reinforce each other. We analyzed the non-Newtonian effect in the simple case of unidirectional parallel plate flow in Example 3.6 where Fig.E 3.6c plots flow rate versus the pressure gradient, illustrating the effect of the shear-dependent viscosity on flow rate using a Power Law model fluid. These curves are equivalent to screw characteristic curves with the cross-channel flow neglected. The Newtonian straight lines are replaced with S-shaped curves. 

The validity of parameter-sets 6 and 8 should additionally be confirmed by using the data from non-isothermal experiments to reject a further possibility in the existence of other parameter-sets with a good degree of fitting. The nonisothermal transient experiments, unfortunately, have not been conducted within the period giving a constant activity of the catalyst. The mode of the transient response curve of N2 is significantly affected by the value of kj, rather than... 

Duff et al. [27] reported a study made by means of DSC and WAXD on SPS/ PPE blends of various compositions, precipitated from ethylbenzene solutions, compression molded at 330 °C for 2 min and then slowly cooled to room temperature. In particular, the WAXD patterns show that in sPS-rich blends (>50 50 wt%) sPS is in a 0 or (3 form, while small amounts of a are present in the 50 50 wt% blend. The kinetics of crystallization and the mechanism of nucleation of sPS were investigated under isothermal and nonisothermal conditions as a function of blend composition and molecular weights of the components. The experimental curves show that the half-time to crystallization, t j2, increases with increasing content and molecular weight of PPE, but is not influenced by the molecular weight of sPS. The crystallization kinetics were... 

Figure 5. Evolution of chemical water during pyrolysis. (Curves) nonisothermal single reaction, first-...

Figure 1. Saran char sample mass history during nonisothermal activation in oxygen. I hc symbols correspond to the scattering curves in Figure 2.

Figure 2. SAXS curv es for saran char during nonisothermal activation in oxygen to 565°C to the indicated mass losses corresponding to the symbols in Figure 1.

Fig. 12.7 (a) Raman spectra and HRTEM images of as-received and vacuum-annealed (graphitized) MWCNTs. As-received nanotubes contain iron particles and amorphous carbon on their surface (inset), (b) Weight loss curves (TGA) of as-received, air-oxidized (0.25 h at 550°C), and graphitized MWCNTs. (c) In situ Raman spectra of nonisothermal oxidation of as-received MWCNTs. All Raman spectra were recorded using 633-nm laser excitation... 

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