Near adiabatic

In Section III.C.5, we give conditions under which Eqs. (9) and (10) are exactly or approximately valid. Noteworthy among these is the nearly adiabatic (slowly evolving) case, which relates to the Deny phase [9]. 

Then, we expect that for this value(s) of the coordinate x, the t zeros of the wavepacket will be located in the upper t half-plane only. The reason for this is similar to the reasoning that led to the theorem about the location of zeros in the near-adiabatic case. (Section rH.E.l). Actually, empirical investigation of wavepackets appearing in the literature indicates that the expectation holds in... 

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

Accelerating Rate Calorimeter (ARC) The ARC can provide extremely useful and valuable data. This equipment determines the self-heating rate of a chemical under near-adiabatic conditions. It usu-aUy gives a conservative estimate of the conditions for and consequences of a runaway reaction. Pressure and rate data from the ARC may sometimes be used for pressure vessel emergency relief design. Activation energy, heat of reaction, and approximate reaction order can usually be determined. For multiphase reactions, agitation can be provided. 

Fig. 13. Comparison of simulated and experimental temperature profiles in a 2-m, near-adiabatic, packed-bed S02 reactor using a Chinese S101 catalyst and operating under periodic reversal of flow direction with r = 180 min, SV = 477 h"1, and inlet S02 = 3.89 vol% and T = 25°C. (Figure adapted from Wu et at., 1996, with permission of the authors.)...

Because process heating is expensive, lagging is invariably applied to heated process vessels to minimise heat loss, particularly during long-term hot storage. Such adiabatic or near-adiabatic systems are potentially hazardous if materials of limited thermal stability, or which possess self-heating capability, are used in them. Insufficiently stabilised bulk-stored monomers come into the latter category. 

If we compare the work required to compress a given gas to a given compression ratio by isothermal and isentropic processes, we see that the isothermal work is always less than the isentropic work. That is, less energy would be required if compressors could be made to operate under isothermal conditions. However, in most cases a compressor operates under more nearly adiabatic conditions (isentropic, if frictionless) because of the relatively short residence time of the gas in the compressor, which allows very little time for heat generated by compression to be transferred away. The temperature rise during an isentropic compression is determined by eliminating p from Eqs. (8-17) and (8-19) ... 

Cauchy-integral method, 219-220 cyclic wave functions, 224-228 modulus and phase, 214-215 modulus-phase relations, 217-218 near-adiabatic limit, 220-224 reciprocal relations, 215-217, 232-233 wave packets, 228-232 multidegenerate nonlinear coupling,... 

Na3F2 cluster, direct molecular dynamics, semiempirical studies, 415 Near-adiabatic limit, molecular systems,... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Time-dependent ground state (TDGS), molecular systems, component amplitude analysis, near-adiabatic limit, 220-224... 

Figure 5 contains experimental profiles of the reaction temperature at the bottom of the sample as a function of time for nearly adiabatic photopolymerizations of Derakane resins containing between 0 and 60 wt.% of the glass fibers. The figure illustrates that for all fiber loadings, upon illumination the temperature exhibits an initial increase from room temperature to a final plateau value around 130°C. Moreover, the figure illustrates that as the fiber loading is increased, both the rate of the initial temperature increase, and the final plateau value, are reduced. These trends are easily explained by the reduction in the reactive fraction of the sample... 

Figure 5. Reaction temperature as a function of time for nearly adiabatic photopolymerizations of vinyl esters with various fiber loadings.

In the Spalding burner, a flat plane flame stands off the surface of a cooled porous matrix. Data are compiled to give Su as measured by the speed in the burner supply, to maintain a stable flame, for a given measured cooling rate. By plotting these data so as to extrapolate to a zero cooling condition yields, S U under nearly adiabatic conditions. 

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