Temperature step increments

In the cooling phase (assuming t. is non-/ero), the velocities are periodically rescaled to change the system temperature from the run temperature to the final temperature Tj in increments of the temperature step AT. The cooling period for rescaling the velocities. P... is defined by ... 

The slope of the volatile = f(final temperature) curve in Figure 1 amounts to volatile increments at particular temperature steps, and is a measure of the pyrolysis rate. The slopes have been obtained by differentiating the volatile curve of Figure 1 for drafting Figure 2. For example, volatiles at 200"C equal 4.6%, and 7.7% at 220"C that is a 3.1% increment in the 20"C step and amounts to a... 

Figure 2 gives rates of pyrolysis in trials with gradually increasing temperatures. In the case of wood heated to 500 C for example, the volatile increments increase from temperature step to temperature step up to 300 C, dropping off in further steps. The sum of the increments reaches 75% at 500 C, as they should according to Figure 1. The area under the curve corresponds to that sum. One can estimate the sum for each final temperature from the areas. For example, in the case of heating to 250 C, the increments average 0.1%, and the sum of the increments becomes 0.1 x (250 - 100) = 0.1 x 150 = 15%, or 0.15 g/g (compare Figure 1).

Fig. 24. Contour plot of the structure factor (the kinematic LEED intensity) of a x y/i monolayer in a triangular lattice gas with nearest-neighbor repulsion, at a temperature k TIi = 0.355 (about 5% above T ) and a chemical potential // = 1.5 (0c = 0.336 at the transition temperature.) Contour increments are in a (common) logarithmic scale separated by 0.1, starting with 3.2 at the outermost contour. Center of the surface Brillouin zon is to the left k, and k the radial and azimuthal components of kH, are in units of nlXla, a being the lattice spacing. Data are based on averages over 2x10 Monte Carlo steps per site. (From Bartelt et...

The "step method. It consists of small successive temperature increments made during the linear increase in temperature with time (Figure 4.6). Each small temperature step is followed by an isothermal delay, which ensures thermal equilibration of the sample. From the difference of the thermal equilibrium aberration between the two cells during a heat pulse, the heat capacity of the sample placed in the working cell can be obtained as a function of temperature. The two crucibles contained in the cells are chosen in such a way so as to have as similar amounts as possible. 

The same experiment should be repeated with two empty cells identical to those used for the experimental sample run (blank experiment). The heat capacity of the sample is obtained at each temperature from the difference between the enthalpy increments obtained at each temperature step, in the two experimental series. 

To further understand the chemical response of both the reaction and the reactor to temperature an experiment was conducted that incorporated several temperature steps. The experiment encompassed stepping the reactor from a starting temperature of 30 °C to a final temperature setting of 60 °C by three separate 10 °C increments. The Raman spectral data from this experiment are plotted in Fig. 9.2.6(a). Note that the ratio between the reactants and products that was so evident in the one temperature step in Fig. 9.2.5(a) is more obscured due to the multiple temperature steps. However, the first scores plot from the PCA analysis. Fig. 9.2.6(b), describes product yield as a function of time and temperature and is full of relevant kinetic and chemical information about the reaction. The PCA data effectively relate the reaction yield efficiency to an increase in reactor temperature. The initial reactor temperature was 30 °C and then the temperature was then systematically stepped to 40, 50 and 60 °C as shown in... 

Running v. Process by which solubility of a resin in an oil is achieved. Eossil resins such as Congo are run by heating the resin alone to elevated temperatures in incremental steps, thereby distilling off unwanted volatile components and altering the resin so that it becomes compatible with additions of oil. Resin so treated are said to have been run . 

In a companion paper (117), the dynamic model of Reference (116) has been completed with account of the SO2 oxidation reaction. For this purpose transient SO2 conversion data were collected over a commercial V-W/Ti02 honeycomb catalyst during SO2 oxidation experiments, involving step changes in temperature, area velocity, and feed composition (SO2, O2, H2O and NH3) with respect to typical DeNOx conditions. Characteristic times of the system response were of a few hours, and peculiar SO3 emission peaks were noted upon step increments of reaction temperature and H2O feed content. All the data could be successfully fitted by a dynamic kinetic model based on the assumption that buildup-depletion of surface sulfate species is rate controlling (see eg. Figure 17). Finally, it was shown that the dynamic model of the SCR monolith reactor in Reference... 

Using a Rheometrics mechanical spectrometer and powdered polymer samples, the authors compared the rheological behaviour of two polymers with similar chemical compositions but different structures. The rheological profiles of polymers 21 and 22 were determined between 140 and 400°C by increasing the temperature at 10°C min from 140 to 190°C and from 300 to 400°C. In the predominant region of isoimide-imide conversion (190-300°C), the temperatme was raised by 2 or 5°C increments, the dynamic viscosity rj being measured at each temperature step. At 190°C, the viscosity of poly(isoimide) 21 was approximately 5 X 10 Pas and decreased to a minimum value of 10 Pas at 243°C as the polymer softened and melted. Thermal conversion to polyimide 22 concurrently... 

This prediction is fulfilled by all the values in Table 9 in every case the value of — kT nK increases throughout the range covered by experiment. Having established this fact, the next step is to look at the rate at which the values of J increase with rise of temperature. For most of the substances in Table 9 values of K are available at 20 and at 40°C. Let us then calculate the values of J at these two temperatures and by subtraction find in each case the increment in J over this range of temperature. From what has been said above we know that we expect the increment in J to depend on whether the proton transfer belongs to class... 

Flynn and Dickens [142] have translated the relaxation methods of fluid kinetics into terms applicable to solid phase thermogravimetry. The rate-determining variables such as temperature, pressure, gas flow rate, gas composition, radiant energy, electrical and magnetic fields are incremented in discrete steps or oscillated between extreme values and the effect on reaction rate determined. 

The temperature profiles along the x-axis at various times are shown in Figure 4. These values should be compared with the theoretical solution T - erfc [ (l-x)/(2jc t) ]. Some numerical oscillations are noted at the heated boundary at short times due to the inability of the rather coarse mesh and time Increment to capture the thermal boundary layer which forms there. However, this can easily be avoided if desired by using a finer mesh in that region, and also by stepping with shorter time increments initially. 

The calculation is performed in terms of degrees Celsius, including values both above and below zero. It is not convenient, therefore, to use the relative increment of temperature as a test for step size in subroutine CHECKSTEP. I use absolute increments instead. At the end of subroutine SPECS, I set incind equal to 3 for all equations, limiting the absolute increment in temperature to 3° per time step. Zonally averaged heat capacity as a function of latitude is calculated in subroutine CLIMINP in terms of land fraction and the heat capacity parameters specified in SPECS. It is returned in the array heap. 

Let us assume a spherical mineral with radius R which initially contains a gas with concentration C0(r), r being the radial distance from the center. Upon incremental heating, this gas is lost to the extraction line and at the ith heating step when time is tf, the fraction of initial gas remaining is/(tf). Loss takes place by radial diffusion with temperature-dependent, hence time-dependent, coefficient 3>(t). We assume that the total amount of gas held by the mineral at t=0 is equal to one, i.e., that... 

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