Temperature lag

Fig. 1 shows the thermal decomposition curves of HDPE mixed with Al-MCM-41, with respect to time, at isothermal operating temperatures. Lag periods were formed at the initial stage of decomposition, possibly due to the heat transfer effect, which could delay the decomposition of a sample until the latter reaches the operating temperatures. As the reaction ten erature increased, the reaction time became noticeably shorter. The shortening of the reaction time was clearly observed when the reaction occurred at the reaction teirperatures between 420 and 460 °C. The HDPE on Al-MCM-41-P decomposed faster than that on blank and that on A1-MCM-41-D, as shown in Fig. 1(b). 

Figure 5 gives the simulation results with the model given for the conditions used by Briggs et al. to obtain Fig. 3. Data points are shown in Fig. 5b, but not in 5a. Mass spectrometer readings were not calibrated, and only normalized data are shown in Fig. 3a. The simulation estimates the shape of the midbed temperature and the SO3 vol% variations successfully. It also reproduces the initial bed temperature lag for the first minute after introduction of the S03/S02 reactant mixture (Fig. 5b), as well as the absence of a lag when air is introduced to the catalyst bed displacing the reactant mixture (Fig. 5a). The model also gives the slow adjustment of the bed temperature after the maximum and minimum temperatures, although the rates of cooling and heating are not correct. The most serious deficiency of the model is that it overestimates the temperature rise and drop by 15 and 8°C, respectively.

If the contact resistance is Rc = 5 x 103 T l [K/W], the time constant r = cA x Rc, due to the contact at the mean temperature of 60 mK, is 120s. Hence the sample temperature lags the bath temperature with a delay of about 120s. 

The TGA system was a Perkin-Elmer TGS-2 thermobalance with System 4 controller. Sample mass was 2 to 4 mgs with a N2 flow of 30 cc/min. Samples were initially held at 110°C for 10 minutes to remove moisture and residual air, then heated at a rate of 150°C/min to the desired temperature set by the controller. TGA data from the initial four minutes once the target pyrolysis temperature was reached was not used to calculate rate constants in order to avoid temperature lag complications. Reaction temperature remained steady and was within 2°C of the desired temperature. The actual observed pyrolysis temperature was used to calculate activation parameters. The dimensionless "weight/mass" Me was calculated using Equation 1. Instead of calculating Mr by extrapolation of the isothermal plot to infinity, Mr was determined by heating each sample/additive to 550°C under N2. This method was used because cellulose TGA rates have been shown to follow Arrhenius plots (4,8,10-12,15,16,19,23,26,31). Thus, Mr at infinity should be the same regardless of the isothermal pyrolysis temperature. A few duplicate runs were made to insure that the results were reproducible and not affected by sample size and/or mass. The Me values were calculated at 4-minute intervals to give 14 data points per run. These values were then used to... 

The state of the art for many polymer processes is a simple time-temperature recipe for the process equipment. This is often a satisfactory solution for processes in which the process equipment temperature and the part temperature are nearly identical. Temperature control for pultrusion of thin cross-sections, for instance, can be satisfactorily based on the die and barrel temperatures. In processes where there is a major difference between the setpoint and the local conditions, it is now becoming more common to implement supervisory controllers which account for these differences. The autoclave curing of composites, for instance, may have large temperature lags between the autoclave and the part as is shown in Figures 15.3... 

Figure 15.3 The temperature lag between autoclave (AIRTC) and composite part (PARTTC) is large, so a supervisory controller is used to drive the autoclave setpoint up and achieve the desired cure cycle in the composite. Because this cure cycle was developed for the autoclave temperature, however, the resin gels before compaction is complete...

At the most rapid heating or cooling rate, the sample temperature lags behind the indicated temperature. 

The furnace in Figure 21-8a performs better than a simple graphite tube. Sample is injected onto a platform that is heated by radiation from the furnace wall, so its temperature lags behind that of the wall. Analyte does not vaporize until the wall reaches constant temperature (Figure 21-8b). At constant furnace temperature, the area under the absorbance peak in Figure 21-8b is a reliable measure of the analyte. A heating rate of 2 000 K/s rapidly dissociates molecules and increases the concentration of free atoms in the furnace. 

One difficulty with DMTA is the potential for uneven temperature distribution and temperature lag when scanning as temperature is ramped up or down. The consequences of lag were considered by Lacik et al48, and methods of calibration using pure substances of known melting point49 and liquid filled polymer matrices50 have been suggested. 

For a monatomic gas, where the heat capacity involves only translational energy, V is independent of sound oscillation frequency (except at ultra-high frequencies, where a classical visco-thermal dispersion sets in). For a relaxing polyatomic gas this is no longer so. At sound frequencies, where the period of the oscillation becomes comparable with the relaxation time for one of the forms of internal energy, the internal temperature lags behind the translational temperature throughout the compression-rarefaction cycle, and the effective values of CT and V in equation (3) become frequency dependent. This phenomenon occurs at medium ultrasonic frequencies, and is known as ultrasonic dispersion. It is accompanied by... 

Figure 3.26 Subtraction technique for elimination of effect of sample heat capacity change. The endotherm from the DTA trace represents both the latent heat of transformation as well as a shift in heat capacity of the sample during the transformation. The baseline (which is the sample temperature lag relative to the reference) shifts most rapidly near the center of the endotherm, where the conversion of reactant to product is most fervent. The right-hand trace represents a DTA endotherm with the effects of sample heat capacity changes subtracted out. Note that in this case, where the total heat capacity of the product is less than the reactant, this subtraction has resulted in an endotherm of larger area.

Figure 3.27 Calculation of heat capacity of an unknown using a Netzsch DSC200 heat-flux DSC [7]. The distinct shift in heat capacity at 690°C corresponds to the glass transition temperature (see section 7.6). A 191 mg sapphire standard was used as calibrant for a 130 mg (laser special) glass sample. All heating ramps were at 20°C/min (faster heating rates permit greater temperature lags). The right hand scale, in the original units of the differential thermocouple, is inverted in exothermic and endothermic directions as compared to the usual convention in this book.

In liquid systems in which reactants are not at the thermostat temperature before mixing there may be considerable temperature lag and consequent error. W. S. Horton, J, Phys. Colloid Che7n., 52,1129 (1948), has made an analysis of these errors for first-order reactions which shows that errors of up to 50 per cent may occur if the initial AT was 10°C. 

Have you ever jumped into a pool of cool water on a hot day early in summer Despite the fact that the air temperature is high, the water temperature lags behind and tends to stay lower. On the other hand, if you return and jump into that same pool in the evening when the air temperature has dropped, the pool water will be warmer than the outside air. 

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