Temperature Profile Studies

The heat release rate dqldt) at any instance from the temperature profile curve is calculated using the following equation  

T2 and Ti are the temperatures corresponding to time tx and ti, respectively, and Cp is the average heat capacity of the solid. The points on the profile curve corresponding to Ti and T2 are chosen very closely so as to obtain an instantaneous rate at these points on the curve. The average data points from four temperature profile measurements are computed to 

From the temperature-time experimental curve, the adiabatic temperature (Tad) at any instant of reaction can be calculated using the following equation  

The exothermicity for each stage is calculated using the expression AH = CpTad. Table 3.13 presents the calculated values of AH at various break points in the temperature profile corresponding to various steps. 

The enthalpy change for the steps involved has been calculated from the temperature profile data and is in agreement with the values obtained from DSC and combustion calorimetry. 

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M. E. Brown and R. A. Rugunanan, A temperature-profile study of the combustion of black powder and its constituent binary mixtures. Propellants, Explosives, Pyrotechnics, 14, 69 (1989). 

However, X-ray powder diffraction of the combustion residue shows it to be a mixture of a- and -Fe203 [19,20]. This is further confirmed by DTA and a temperature profile study that revealed an exotherm at 630°C corresponding to the conversion of —>a-Fe203. 

Nonisothermal Gas Absorption. The computation of nonisothermal gas absorption processes is difficult because of all the interactions involved as described for packed columns. A computer is normally required for the enormous number of plate calculations necessary to estabUsh the correct concentration and temperature profiles through the tower. Suitable algorithms have been developed (46,105) and nonisothermal gas absorption in plate columns has been studied experimentally and the measured profiles compared to the calculated results (47,106). Figure 27 shows a typical Hquid temperature profile observed in an adiabatic bubble plate absorber (107). The close agreement between the calculated and observed profiles was obtained without adjusting parameters. The plate efficiencies required for the calculations were measured independendy on a single exact copy of the bubble cap plates installed in the five-tray absorber. 

On the other hand, this type of cooling permits the study of increasing or decreasing temperature profiles in the jacket and their influence on the inner temperature profile, reactor performance, and stability. For this type of study a reactor tube is needed that is large enough to accommodate an inner thermowell holding a multiple thermocouple assembly. 

Ethylene oxidation was studied on 8 mm diameter catalyst pellets. The adiabatic temperature rise was limited to 667 K by the oxygen concentration of the feed. With the inlet temperature at 521 K in SS and the feed at po2, o=T238 atm, the discharge temperature was 559 K, and exit Po =1.187 atm. The observed temperature profiles are shown on Figure 7.4.4 at various time intervals. The 61 cm long section was filled with catalyst. 

VFO works well in gas turbines. In a nine-month test program, the combustion properties of VFO were studied in a combustion test module. A gas turbine was also operated on VFO. The tests were conducted to study the combustion characteristics of VFO, the erosive and corrosive effects of VFO, and the operation of a gas turbine on VFO. The combustion tests were conducted on a combustion test module built from a GE Frame 5 combustion can and liner. The gas turbine tests were conducted on a Ford model 707 industrial gas turbine. Both the combustion module and gas turbine were used in the erosion and corrosion evaluation. The combustion tests showed the VFO to match natural gas in flame patterns, temperature profile, and flame color. The operation of the gas turbine revealed that the gas turbine not only operated well on VFO, but its performance was improved. The turbine inlet temperature was lower at a given output with VFO than with either natural gas or diesel fuel. This phenomenon is due to the increase in exhaust mass flow provided by the addition of steam in the diesel for the vaporization process. Following the tests, a thorough inspection was made of materials in the combustion module and on the gas turbine, which came into contact with the vaporized fuel or with the combustion gas. The inspection revealed no harmful effects on any of the components due to the use of VFO. 

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as T, and the temperature of the outer surface of the steam coil as U then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

This study was run in a laboratory bench-scale unit with 0.75-in. reactor tubes. The catalysts were sized to 10 X 12 mesh and diluted nine-to-one with Si02 in order to spread the reaction out through the bed and to permit measurement of temperature profiles, the profile being an... 

It is impossible to solve these partial differential equations with the varied input conditions resulting from the California cycle. A computer was used in the study, where distance is divided into increments of 0.08 to 0.30 in. in thickness, and time is divided into increments of 0.4 sec. They obtained the temperature profile in the bed as a function of time from a cold start. This procedure could result in a very long computation, as the California cycle has a duration of 16 min, requiring 2400 time intervals and computations. 

More recently, Rosen (R3), Spalding (S5), and Johnson and Nachbar (J4) have considered a simplified approach using the analysis of laminar-flame propagation velocities. According to these investigators, the principal exothermic reactions occur in the gas phase. Some of the heat liberated by these reactions is then transferred back to the solid surface to sustain the endothermic surface-gasification processes. Thus, the temperature profile within the reactive zone is quite similar to that of Rice and Crawford. However, gasification of the solid surface is assumed to be endothermic, while exothermic reactions were considered in the studies discussed previously. 

The basic approach taken in the analytical studies of composite-propellant combustion represents a modification of the studies of double-base propellants. For composite propellants, it has been assumed that the solid fuel and solid oxidizer decompose at the solid surface to yield gaseous fuel and oxidizing species. These gaseous species then intermix and react in the gas phase to yield the final products of combustion and to establish the flame temperature. Part of the gas-phase heat release is then transferred back to the solid phase to sustain the decomposition processes. The temperature profile is assumed to be similar to the situation associated with double-base combustion, and, in this sense, combustion is identical in the two different types of propellants. 

An implicit assumption of the foregoing treatment is that A// remains independent of temperature over the range investigated. This is very nearly correct in general, and is particularly the case given that studies of reactions in solution are usually conducted over a temperature interval of only some 30-50°. In certain circumstances the temperature profiles show curvature outside the experimental error. Such cases have, or appear to have, temperature-dependent activation enthalpies. Here we explore one of the reasons for that another is given in Section 7.3. 

For the analysis of the chemical structure of flames, laser methods will typically provide temperature measurement and concentration profiles of some readily detectable radicals. The following two examples compare selected LIF and CRDS results. Figure 2.1 presents the temperature profile in a fuel-rich (C/O = 0.6) propene-oxygen-argon flame at 50 mbar [42]. For the LIF measurements, 1% NO was added. OH-LIF thermometry would also be possible, but regarding the rather low OH concentrations in fuel-rich flames, especially at low temperatures, this approach does not capture the temperature rise in the flame front [43]. The sensitivity of the CRDS technique, however, is superior, and the OH mole fraction is sufficient to follow the entire temperature profile. Both measurements are in excellent agreement. For all flames studied here, the temperature profile has been measured by LIF and/or CRDS. 

A main objective of the work of Hardt et al. was to study the influence of heat transfer on the achievable molar flux per unit reactor volume of the product species. They compared unstructured channels to channels containing micro fins such as shown in Figure 2.31. Heat transfer enhancement due to micro fins resulted in a different axial temperature profile with a higher outlet temperature in the reaction gas channel. Owing to this effect and by virtue of the temperature dependence... 

With dt = 0.025 m study the effect of varying inlet temperature (Tq = 600, 640, 660 K, with constant jacket temperature. Note the hot spot effect in the reactor temperature profile. 

Study the effect of jacket temperature on the temperature profile, by keeping Tq constant and varying Tj. 

In a recent study, Huan et al. [25] performed NM R experiments in vibrofluidized beds of mustard seeds in which the small sample volume allowed pulses short enough that displacements in the ballistic phase were distinguishable from those in the diffusion phase. In this case, the average collision frequency is measured directly, bypassing the uncertainty of the multiplicative factor mentioned above. These workers also measured the height dependence of the granular temperature profile. 

Ehase Inversion Temperatures It was possible to determine the Phase Inversion Temperature (PIT) for the system under study by reference to the conductivity/temperature profile obtained (Figure 2). Rapid declines were indicative of phase preference changes and mid-points were conveniently identified as the inversion point. The alkane series tended to yield PIT values within several degrees of each other but the estimation of the PIT for toluene occasionally proved difficult. Mole fraction mixing rules were employed to assist in the prediction of such PIT values. Toluene/decane blends were evaluated routinely for convenience, as shown in Figure 3. The construction of PIT/EACN profiles has yielded linear relationships, as did the mole fraction oil blends (Figures 4 and 5). The compilation and assessment of all experimental data enabled the significant parameters, attributable to such surfactant formulations, to be tabulated as in Table II. 

The concentration profile studies find that the hydrogen diffusion coefficient in a-Si H is thermally activated, as shown in Fig. 17 (Street et al., 1987). Over the temperature range of 130 to 300°C, the diffusion data is described by the Arhennius expression... 

In situ temperature profiles during the photopolymerizations were obtained using a high-speed thermocouple system (WB-AAI-B8 interface card, Omega Systems) which was interfaced with a personal computer. For these studies, the... 

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