Characteristic temperature adiabatic

In the last analysis, self-heating chemicals are classified into the two large groups, the TD and the AC type, but in fact they are subdivided into the following four groups in all, in accordance with the difference in the selfheating process which, when subjected to the adiabatic self-heating test started from a T, 2 cm each of them each show, or, in accordance with the difference in the characteristic temperature, i.e., the Tc or the SADT, to express each individual thermal instability, as presented in Table 3. 

In the foregoing discussion we have seen how the case Ma 0 with an adiabatic wall is an example of incompressible flow. In other instances there is significant heat transfer through the wall. In this case we can isolate the flow situation by imagining that the wall is held at some fixed temperature Tw that is different from Tq. The non-dimensional scale for the temperature is redefined, so we need to redo the analysis of the resulting dimensionless equations. The problem now has a characteristic temperature scale, To — Tw, which is a driving force for the conduction of heat from the wall into the fluid. Since we expect that all temperatures will lie between these two values, the proper non-dimensional temperature is T =. The temperature... 

Dehydrogenation of ethylbenzene to styrene is normally accomplished in a fixed-bed reactor. A catalyst is packed in tubes to form the fixed bed. Steam is often fed with the styrene to moderate the temperature excursions that are characteristic of adiabatic operation. The steam also serves to prolong the life of the catalyst. Consider the situation in which we model the behavior of this reactor as an isothermal plug flow reactor in which the dehydrogenation reaction occurs homogeneously across each cross section of the reactor. The stoichiometry of the primary reaction is... 

The relation (184 111) could be considered a definition of a characteristic temperature Tj corresponding to Eyring s formulation of activated complex theory /20b/. However, when the non-adiabatic condition (72.Ill) is really fulfilled, equation (184.III) actually represents only a relation of equivalency of the collision and statistical formulations of reaction rate theory in the high temperature region T >T /2 to which both the formulas (177.Ill) and (183.Ill) refer. This means that if T < T, the formula (183.III) cannot be used in the temperature range TjJ/2 < T < Tj /2 for physical reasons. 

It may be remarked that the equilibration between the different forms of energy of a system of molecules which are not undergoing reaction is usually attained quite rapidly due to the coUisional process. It is only under rather exceptional conditions that the equilibration is not attained, for example, in flames or in the rapid adiabatic compressions due to sound waves. In the latter instance the vibrational energy does not attain equilibrium with the translational (and rotational) energy within the period of the wave. Under such conditions it may occur that the various translational states are at approximate equilibriiun with each other and have a statistical parameter 7, and also that the vibrational states are at equilibrium amongst themselves with a characteristic temperature However, if... 

Adiabatic operation. If adiabatic operation leads to an acceptable temperature rise for exothermic reactors or an acceptable fall for endothermic reactors, then this is the option normally chosen. If this is the case, then the feed stream to the reactor requires heating and the efiluent stream requires cooling. The heat integration characteristics are thus a cold stream (the reactor feed) and a hot stream (the reactor efiluent). The heat of reaction appears as elevated temperature of the efiluent stream in the case of exothermic reaction or reduced temperature in the case of endothermic reaction. 

Heat carriers. If adiabatic operation produces an unacceptable rise or fall in temperature, then the option discussed in Chap. 2 is to introduce a heat carrier. The operation is still adiabatic, but an inert material is introduced with the reactor feed as a heat carrier. The heat integration characteristics are as before. The reactor feed is a cold stream and the reactor efiluent a hot stream. The heat carrier serves to increase the heat capacity fiow rate of both streams. 

Oxidizers. The characteristics of the oxidizer affect the baUistic and mechanical properties of a composite propellant as well as the processibihty. Oxidizers are selected to provide the best combination of available oxygen, high density, low heat of formation, and maximum gas volume in reaction with binders. Increases in oxidizer content increase the density, the adiabatic flame temperature, and the specific impulse of a propellant up to a maximum. The most commonly used inorganic oxidizer in both composite and nitroceUulose-based rocket propellant is ammonium perchlorate. The primary combustion products of an ammonium perchlorate propellant and a polymeric binder containing C, H, and O are CO2, H2, O2, and HCl. Ammonium nitrate has been used in slow burning propellants, and where a smokeless exhaust is requited. Nitramines such as RDX and HMX have also been used where maximum energy is essential. 

The curve in Figure 21 represents SO2 equiUbrium conversions vs temperature for the initial SO2 and O2 gas concentrations. Each initial SO2 gas concentration has its own characteristic equiUbrium curve. For a given gas composition, the adiabatic temperature rise lines can approach the equiUbrium curve but never cross it. The equiUbrium curve limits conversion in a single absorption plant to slightly over 98% using a conventional catalyst. The double absorption process removes this limitation by removing the SO from the gas stream, thereby altering the equiUbrium curve. 

Two isotherms, isochores, adiabatics, or generally any two thermal lines of the same kind, never cut each other in a surface in space representing the states of a fluid with respect to the three variables of the characteristic equation taken as co-ordinates, for a point of intersection would imply that two identical states had some property in a different degree (e.g., two different pressures, or temperatures). Two such curves may, however,... 

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

Two-dimensional compressible momentum and energy equations were solved by Asako and Toriyama (2005) to obtain the heat transfer characteristics of gaseous flows in parallel-plate micro-channels. The problem is modeled as a parallel-plate channel, as shown in Fig. 4.19, with a chamber at the stagnation temperature Tstg and the stagnation pressure T stg attached to its upstream section. The flow is assumed to be steady, two-dimensional, and laminar. The fluid is assumed to be an ideal gas. The computations were performed to obtain the adiabatic wall temperature and also to obtain the total temperature of channels with the isothermal walls. The governing equations can be expressed as... 

For the adiabatic condition in which RHL is suppressed, the flame response exhibits the conventional upper and middle branches of the characteristic ignition-extinction curve, with the upper branch representing the physically realistic solutions. It can be noted that the effective Le of this lean methane/air mixture is sub-unity. It can be seen from Figure 6.3.1 that, with increasing stretch rate, first increases owing to the nonequidiffusion effects (S > 0), and then decreases as the extinction state is approached, owing to incomplete reaction. Furthermore, is also expected to degenerate to the adiabatic flame temperature, when v = 0. 

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

In practice, nearly all reactors used for the manufacture of fine chemicals are neither isothermal nor adiabatic. The temperature-versus-time (location) profile is determined by the kinetic and physical characteristics of the reaction mixture as well as by the reactor geometry and hydrodynamics. The relationships governing this profile will be discussed in Section 5.4.2. 

Cold shot. Injection of cold fresh feed for exothermic reactions or preheated feed for endothermic reactions to intermediate points in the reactor can be used to control the temperature in the reactor. Again, the heat integration characteristics are similar to adiabatic operation. The feed is a cold stream if it needs to be increased in temperature or vaporized and the product a hot stream if it needs to be decreased in temperature or condensed. If heat is provided to the cold shot or hot shot streams, these are additional cold streams. 

The RC1 reactor system temperature control can be operated in three different modes isothermal (temperature of the reactor contents is constant), isoperibolic (temperature of the jacket is constant), or adiabatic (reactor contents temperature equals the jacket temperature). Critical operational parameters can then be evaluated under conditions comparable to those used in practice on a large scale, and relationships can be made relative to enthalpies of reaction, reaction rate constants, product purity, and physical properties. Such information is meaningful provided effective heat transfer exists. The heat generation rate, qr, resulting from the chemical reactions and/or physical characteristic changes of the reactor contents, is obtained from the transferred and accumulated heats as represented by Equation (3-17) ... 

The Accelerating Rate Calorimeter (ARC ) is another adiabatic test instrument that can be used to test small samples. The ARC with the clamshell containment design can handle explosive compounds. It is a sensitive instrument that can indicate the onset of exothermicity where the reaction mixture can be accurately simulated (HSE 2000). ARC testing results can be used in determining a time to maximum rate of decomposition, as well as in calculating a temperature of no return for a container or vessel with specific heat removal characteristics. Further information and references related to the ARC are given in CCPS (1995a) and Urben (1999). 

FIGURE 6.11 Characteristic parametric variations of dimensionless temperature T and mass fraction m of fuel, oxygen, and products along a radius of a droplet diffusion flame in a quiescent atmosphere. j is the adiabatic, stoichiometric flame temperature, pA is the partial density of species A, and p is the total mass density. The estimated values derived for benzene are given in Section 2b. 

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