Heat Release Curves

The heat release curve is then broken up into zones. Temperatures for these zones are selected so that straight lines drawn between the temperature points will approximate the curve. The greatest care should be taken when the shell plot and the tube plot come the closest together. Usually, three to five points are sufficient if a curve of this nature is done by hand. If the MTD is being calculated on the computer, more points are usually used. 

If there were just a small curvature for the condensing fluid, the zones would be figured as a counterflow exchanger and then the normal overall correction factor would be used in each zone. This assumes the correction factor for each zone is the same as the overall. 

With a large hump in the condensing curve, you cannot apply the same correction factor to each zone nor can you take each counterflow zone and calculate a correction factor fi om the counterflow temperatures. This would give an inaccurate At, particularly in the low At zone next to the shell outlet. 

This method gives good results and requires a minimum of time. Here the terminal tube temperatures (tj and t2) are used with each zone to calculate both the MTD and the correction factor. For the limiting case of single phase, linear fluids it will give the same result as applying the customary correction factor to the overall counterflow MTD. 

The method checks closely with the long trial and error method, even when the hot and cold outlet temperatures are the same. 

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Owing to this large concentration of OH relative to O and H in the early part of the reaction zone, OH attack on the fuel is the primary reason for the fuel decay. Since the OH rate constant for abstraction from the fuel is of the same order as those for H and O, its abstraction reaction must dominate. The latter part of the reaction zone forms the region where the intermediate fuel molecules are consumed and where the CO is converted to C02. As discussed in Chapter 3, the CO conversion results in the major heat release in the system and is the reason the rate of heat release curve peaks near the maximum temperature. This curve falls off quickly because of the rapid disappearance of CO and the remaining fuel intermediates. The temperature follows a smoother, exponential-like rise because of the diffusion of heat back to the cooler gases. 

If the initial pressure is increased to some value P2, the heat release curve shifts to higher values, which are proportional to P" (or p"). The assumption is made that h is not affected by this pressure increase. The value of P2 is selected so that the ql becomes tangent to the qr curve at some point c. If the value of h is lowered, qr is everywhere greater than ql and all initial temperatures give explosive conditions. It is therefore obvious that when the ifo line is tangent to the qr curve, the critical condition for mixture self-ignition exists. 

FIGURE 8.8 Rate of heat release curves of PU-nanocomposite coatings on PET knitted fabrics at 35kW/m2. (From Devaux, E. et al., Fire Mater., 26, 149, 2002. With permission.)... 

FIGURE 8.10 Rate of heat release curves of TPU, TPU/DP-POSS, and TPU/FQ-POSS as coating of woven PET fabrics at heat flux 35kW/m2. (From Bourbigot, S. et al., Fire Retardancy of Polymers New Applications of Mineral Fillers, Bras, M., Bourbigot, S., Duquesne, S., Jama, C., and Wilkie, C.A., Eds., The Royal Society of Chemistry, Cambridge, MA, 2005, 189. With permission.)... 

The methods presented above are applicable only for conditions in which the heat transferred is a straight-line function of temperature. For systems that do not meet this condition, the total heat-release curve can be treated in sections, each section of which closely approximates the straight-line requirement. A log mean temperature difference can then be calculated for each section. Common examples in which this approach is encountered include (1) total condensers in which the condensate is subcooled after condensation, and (2) vaporizers in which the fluid enters as a subcooled liquid, the liquid is heated to the saturation temperature, the fluid is vaporized, and the vapor is heated and leaves in a superheated state. 

For the CSTR model, the highest intersection point is physically realistic and, indeed, important. It corresponds to an intersection point on the deceleratory part of the reaction rate curve as indicated in Fig. 5.6(a, b). There are now two possible tangencies of the heat loss line with the heat release curve as some parameter such as the residence time is varied, as indicated in the figure. The first has a similar implication as in the Semenov case. It corresponds to the merger of two low-lying steady-states and to an ignition point on the steady-state locus and, in this model, arises typically as the residence time is increased. The system now jumps to a high steady-... 

Equipment Design Handbook Heat Release Curves... 

Usually, a prerequisite for determining a weighted MTD is a heat release curve. It is used for a guide in determining where to zone the heat transfer calculations. A heat release curve is a plot of heat load vs. temperature of both shell and tube fluids. An example of this can be seen in Figure 2-21. 

Example. Figure 2-24 is a heat release curve for a combined feed exchanger in a Platformer. For the first trial, run through the procedure for finding the number of shells in series. If the last tie line intersects T2, you need no more trials. 

Pick out one of the exchangers represented on the curve. It is best to pick out a middle exchanger and one where the heat release curve is the easiest to read if the heat release curve is quite erratic. Choose four adjacent temperature points as represented by intercepted points on the curve. All will give approximately the same correction factor. For example, the terminal temperatures of the hottest shell will be Tj, T, t2 and ta. For purpose of illustration, we will use these to calculate the correction factor. 

Figures 4.23(a) and (b) show the individual elements of the heat released during the reaction while Figure 4.23(c) shows the composite total heat release curve for the reaction.

When the addition of diethyl propylmalonate is started, the heat output of the reaction is compensated by the jacket cooling shown by the positive heat flow (A) in Figure 4.23(a). As the reaction proceeds a sharp decrease (B) in Figure 4.23(a) occurs coincidental with nucleate boiling which is shown by the increase (B) in the reflux heat release curve in Figure 4.23(b). The heat flow... 

In order to obtain the overall heat release profile for the reaction it is necessary to combine these two power output traces. The composite heat release curve is shown in Figure 4.23(c). The two dips in the trace, (G and H in Figure 4.23(c)), are due to a phase difference between the measurement of the heat flow and reflux data. 

Consider (Fig. 7.4.1) a plot of rate of heat release (Curve 1) versus temper-... 

The Li-ion power tool packs exhibited a fire development trend similar to the CUP commodity. A delay in fire growth occurred at 55 s as the flames penetrated the cartons and the plastic components of the battery packs became involved in the fire. This delay was observed as a temporary plateau in the heat release curve from 55 to 75 s. The fire then grew steadily from 75 s until the lire reached a maximum of 1,900 kW. The fire size then decreased to approximately 1,250 kW, remained steady, and then decreased as a majority of the combustibles were consumed. 

The following experiment provides further verification that the non-simple time dependence of the heat release for PS is due to energy states excited above 15 K and depopulation during the cooling process, very likely through thermally activated relaxation. We have charged the sample at 80 K for several hours and cooled it then to 1 K. We have left the sample for 22 h at 1 K and later continued to 0.3 K, the temperature at which the heat release was measured (Curve (1) in Fig. 4.19). We observe now a clear deviation from the r law. That means that even after 22 h at 1 K the energy states excited above 15 K have not relaxed completely. After 60 h at 0.3 K we warmed the sample to 1 K for 17 h, cooled it to 0.3 K and measured the heat release (Curve (2) in Fig. 4.19). The heat release follows the theoretical r -dependence very well. 

The mechanism of influence of NO2 on the oxidation and spontaneous combustion of hydrocarbons, primarily at low pressures, was discussed in detail in [13]. For the slow oxidation of methane, as in the case of other alkanes, addition of NO2 was demonstrated to shorten or even eliminate (starting from a certain amount) the induction period, causing no changes in the qualitative and quantitative composition of the oxidation products. For the oxidation of a 15% CH4—85% air mixture at T = 480—510 °C and P = 300 Torr in the presence of a small (1.37%) NO2 additive, the heat-release curve featured two peaks [175], the first of which, according to the authors, is associated with the formation of formaldehyde, whereas the second, with its decomposition. This explanation is difficult to accept, because in the absence of NO2, the formation and decomposition of formaldehyde also occur, but no double peak is observed. A double exothermic peak in the oxidation of methane in the presence of NO2 was observed in [176] and for the oxidation of propane in [177]. 

Given that fractal dimension obviously affects the elastic properties of the fat, the important question to ask is. Can processing conditions be used to change the fractal dimension of a particular fat and therefore its elastic properties If we deviate from experimental evidence for a moment and consider Figure 10, which shows two idealized heat release curves during crystallization of a hypothetical fat, it is possible to explain one way in which the order in the microstructural elemental packing can be increased. When a crystallization event occurs, there is the concomitant release of the heat of crystallization. If this heat is released... 

Figure 27 Heat release curves of polyethylene modified with DECA, AO, and ZnAl-LDH. Reprinted from Manzi-Nshuti, C. Hossenlopp, J. M. Wilkie. C. A. Polym. Degrad. Stab. 2009, 94 (5), 782, with permission from Elsevier.

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