Temperature axial gradient

Substantial heat-transfer intensification was also described for a special micro heat exchanger reactor [104]. By appropriate distribution of the gas-coolant stream, the axial temperature gradient can be decreased considerably, even under conditions corresponding to very large adiabatic temperature rises, e.g. of about 1400 °C. 

C) [103]. For this reason, pulses of high 1-butene concentration were inserted in the micro reactor. Remarkably low axial temperature gradients within the explosion regime at high thermal power were found. The zone of the highest reaction rate shifts with respect to the micro channel length. 

Apply the conservation of energy, Equation (3.40). Since the control volume is fixed the pressure work term does not apply. The shear work (v x shear force) is zero because (a) the radius of the control volume was selected so that the velocity and its gradient are zero on the cylindrical face and (b) at the base faces, the velocity is normal to any shear surface force. Similarly, no heat is conducted at the cylindrical surface because the radial temperature gradient is zero, and conduction is ignored at the bases since we assume the axial temperature gradients are small. However, heat is lost by radiation as... 

The axial temperature gradient is fixed by the furnace settings because the gas heat-up lengths are small and most heat transfer occurs by radiation at LPCVD conditions. 

Although an optimum temperature profile may be specified from theoretical calculations, it may not be possible to achieve in practice. The maximum temperature which can be used is usually determined by the materials of reactor construction or the durability of a catalyst. Also, steep axial temperature gradients cannot be realised unless heat transfer rates are high. If heat transfer is poor and the overall process is exothermic, temperature programming of a single reactor may be impossible the reactor becomes virtually adiabatic. In cases such as these, staged reactors (discussed elsewhere in this volume) with intercoolers may be used as a compromise. 

Several theoretical and empirical studies have been made of the impact of column ovens on separations [84]. The two most important factors that must be considered are the preheating of the mobile phase before it enters the column and the extra-column volume between the injector and the column. Work by Djordevic et al. [76] provides some of the most dramatic evidence for the impact of pre-heating the mobile phase. Their measurements of the axial temperature gradient in 4.6 mm columns at typical flow rates are shown in Table 9.2. 

Measured Axial Temperature Gradients for a 4.6 mm i.d. Column at Three Temperatures with and without a 4.5 m x 0.5 mm i.d. Preheater... 

Both radial and axial temperature gradients may appear. As shown is Section 16.3.5, adsorption of polymers depends on temperature. Given the temperature and pressure dependence of the preferential sorption of the mixed eluent components within column packing [146-149], one can expect also considerable changes in the column interactivity with the temperature and pressure variations that may result in a possible gradual departure from the critical conditions. 

Analysis of Heat Transfer. In the vertical Bridgman-Stockbarger system shown in Figure la, the axial temperature gradient needed to induce solidification is created by separating hot and cold zones with a diabatic zone in which radial heat flow from the ampoule to the furnace is suppressed. Analyses of conductive heat transfer have focused on this geometry. 

Heat-Transfer Analysis Thermal-Capillary Models. Numerous analyses of various aspects of heat transfer in the CZ system have been reported many of these are cited by either Kobayashi (143) or Derby and Brown (144). The analyses vary in complexity and purpose, from the simple one-dimensional or fin approximations designed to give order-of-magni-tude estimates for the axial temperature gradient in the crystal (98) to complex system-oriented calculations designed to optimize heater design and power requirements (145,146). The system-oriented, large-scale calculations include radiation between components of the heater and the crucible assemblies, as well as conduction and convection. 

In the case of stacks, radiation plays an even more role important than in the case of a single cell. In fact, in addition to differences in the axial temperature gradients there are differences between the operating temperatures of adjacent cells. A detailed explanation of a radiation model is proposed in the last section. 

Typically the interphase temperature gradients are substantially smaller than the radial and axial temperature gradients, being on the order of 1 to 3°C, and can often be neglected. 

The primary concern for accurate thermal conductivity measurements using this technique is to eliminate axial heat flow. As long as the central heater is long, its temperature near the central portion is uniform. Devoid of an axial temperature gradient, heat will strictly flow radially outward from the central... 

Tubular Reactors. The simplest model of a tubular reactor, the plug-flow reactor at steady state is kinetically identical to a batch reactor. The time variable in the batch reactor is transformed into the distance variable by the velocity. An axial temperature gradient can be imposed on the tubular reactor as indicated by Gilles and Schuchmann (22) to obtain the same effects as a temperature program with time in a batch reactor. Even recycle with a plug flow reactor, treated by Kilkson (35) for stepwise addition without termination and condensation, could be duplicated in a batch reactor with holdback between batches. 

The second boundary condition has been satisfied by noting that the axial temperature gradient dT/dx is constant. The temperature distribution may finally be written in terms of the temperature at the center of the tube ... 

The temperature of an FFB regenerator rises gradually from the bottom to the top with an axial temperature gradient of 20-40°C, as compared to less than 10°C for the turbulent bed. The calculated temperature in the bottom zone should be in the neighborhood of 600°C by the assumption of perfect mixing of catalyst and air streams without any backmixing, yet it is far beyond the actual measured temperature. Therefore, ideal plug flow does not exist in the whole FFB, especially in the bottom zone, but the extent of mixed flow is nevertheless much less than that of TB. 

For an exothermic reaction the gas now entering at O will be heated as it flows over the hot bed, and the bed is cooled. Reaction then occurs as the E end is approached, and the gas leaves with the appropriate conversion at E. The O end of the reactor now has an axial temperature gradient resulting from the passage of the cool gas. At an appropriate moment the reactive gas is switched back to E. The feed is now heated by the hot catalyst and reacts, but further down the bed it encounters the cold catalyst layers, where its conversion continues to increase for a reversible exothermic reaction such as the oxidation of SO2. Before the temperature at O... 

It can be seen from Fig. 27 that, although the gels are thermostatted, the electrolyte solutions are kept at room temperature. This leads to a continuous axial temperature gradient between these solutions and the gels, but in the gels and in the buffer just above and just below the gel the temperature is constant. 

Reaction Procedures. All reaction studies were performed with reactor-equilibrated catalyst samples. A standard catalyst charge weighed between 100 and 125 milligrams with an average particle diameter of 275 microns. The catalyst bed was centered between two beds of quartz particles with the same average particle diameter as the catalyst. The quartz beds were used to thermally insulates the catalyst and reduce the axial temperature gradient (< 5°C) across the catalyst bed. 

The axial temperature gradient is an order of magnitude smaller than the radial temperature gradient, hence the axial conduction in the fuel, gap, and clad is negligible. 

---