Fluctuation temperature

Model of ID dissipation spectrum from Pope [19] (line) and measured, noise-corrected spectrum of the square of the radial gradient of fluctuating temperature in a CH4/I-I2/N2 jet flame (Re = 15,200) (symbols). Each spectrum is normalized by its maximum value. The arrow indicates the 2% level, which corresponds to the normalized wavenumber k = 1 according to the model spectrum. (From Barlow, R.S., Proc. Combust. Inst., 31, 49,2007. With permission.)... 

This set of equations is solved by ODE with t = 5. For comparison, the case with constant input temperature also is done. The steady state effluent concentration is 0.255 at constant temperature, but falls to 0.22 on the average with fluctuating temperature. The difference between these values of course can be reduced by reducing the temperature fluctuations which are high,... 

Comparing the mean field (12) and the fluctuation (15) contributions to the specific heat (in the low and high temperature limiting cases one may use Eqs. (22), (24)) we may estimate the fluctuation temperature < Tc, at which the contribution of fluctuations of the order parameter becomes to be as important as the mean field one (so called Ginzburg - Levanyuk criterion),... 

There are many different aspects to the field of turbulent reacting flows. Consider, for example, the effect of turbulence on the rate of an exothermic reaction typical of those occurring in a turbulent flow reactor. Here, the fluctuating temperatures and concentrations could affect the chemical reaction and heat release rates. Then, there is the situation in which combustion products are rapidly mixed with reactants in a time much shorter than the chemical reaction time. (This latter example is the so-called stirred reactor, which will be discussed in more detail in the next section.) In both of these examples, no flame structure is considered to exist. 

TNC.4. I. Prigogine, Thermodynamics of Irreversible Processes and Fluctuations, Temperature 2, 215-232 (1955). 

Lockwood, F. C., and H. A. Moneib. 1980. Fluctuating temperature measurement in a heated round hee jet. Combustion Science Technology 22 63-81. 

Such a method has been additionally developed. The method uses the mean values of temperature and species concentrations and applies a presumed PDF, to obtain the mean reaction rate. The PDF takes into account the effect of fluctuating temperature on the mean reaction rate. 

However, the intra-atomic Coulomb interaction Uf.f affects the dynamics of f spin and f charge in different ways while the spin fluctuation propagator x(q, co) is enhanced by a factor (1 - U fX°(q, co)) which may exhibit a phase transition as Uy is increased, the charge fluctuation propagator C(q, co) is depressed by a factor (1 -H UffC°(q, co)) In the case of light actinide materials no evidence of charge fluctuation has been found. Most of the theoretical effort for the concentrated case (by opposition to the dilute one-impurity limit) has been done within the Fermi hquid theory Main practical results are a T term in electrical resistivity, scaled to order T/T f where T f is the characteristic spin fluctuation temperature (which is of the order - Tp/S where S is the Stoner enhancement factor (S = 1/1 — IN((iF)) and Tp A/ks is the Fermi temperature of the narrow band). 

This procedure can be utilized to determine whether heavy fuel wax crystal modifiers will lose their performance properties after long-term storage at fluctuating temperatures. Daily heating and overnight cooling may interfere with the ability of some wax crystal modifiers to maintain their performance properties in some residual oils and crude oils. This loss of performance is frequently termed pour point reversion. The British Admiralty Pour Point Test can be utilized to help predict these reversion tendencies. 

The methods of analysis involving numerical solutions appear sufficiently well advanced to permit a rapid expansion of the microscopic analysis of turbulent transport as soon as some of the basic experimental facts are obtained. The next advance of particular interest to the chemical engineer appears to be an understanding of the kinetics of chemical reactions in turbulent flow. The fluctuating temperatures and concentrations introduce perturbation in the normal approach to kinetics that may well yield interesting results in the field of combustion and perhaps in chemical processing. 

SAN polymers exhibit high stiffness, dimensional stability and resistance to fluctuating temperatures. 

Dimensional stability must be good over wide or fluctuating temperature ranges. 

Figure 8. The spin-fluctuation temperature, Tsf, of UPt3 as a function of the pressure-induced relative change in the c/a ratio a comparison is made with the shift in Tsf by the relative change in the c/a ratio induced by substituting Pt by Pd and Th in U( Pt,Pd)3, respectively data from ref.[35].

The overall combustor/optical layout is shown in Fig. 3, which illustrates temperature measurement by the Stokes/anti-Stokes method. Typical results for temperature pdf s at four radial positions (2, 7) near the centerline to near the flame boundary - and at an axial distance 50 fuel-tip diameters downstream of the fuel line tip are shown in Fig. 4. The shaded parts of the pdf contours (from 300 to 800°K), which increase in area near the flame boundary, correspond substantially to scattering from ambient temperature air, and therefore provide a measure of flow intermittency. The upper limit of these bins was chosen to be 800°K because the accuracy possible for the Stokes/anti-Stokes temperature measurement method degrades rapidly at temperatures below roughly that value (2,2) Thus, treating the fluctuation temperature data for T < 800 K in any greater detail was unwarranted. 

The emphasis in this work has been on the acquisition of simultaneously-obtained instantaneous values of temperature and concentration, with as high a spatial resolution as practical for such experiments. The temporal and spatial resolution requirements result from the necessity to probe within (if at all possible) characteristic turbulence time and length scales. The accuracy of our experiments (which, in any case, utimately depends upon a trade-off with resolution (1)), is considered to be adequate to achieve the diagnostic goal of providing data of value to flame modelers this can be seen by comparison of the fluctuation temperature measurement uncertainty (characterized by a 5-7% standard deviation) with the broad temperature spread of the measured pdf s (extending, in Fig. 4, from values near ambient temperature to values in the vicinity of the adiabatic flame temperature). ... 

T.P. Labuza, K. Bohnsack, and M.N. Kim, Kinetics of protein quality change in egg noodles stored under constant and fluctuating temperatures. Cereal Chem., 1982, 59, 142-147. 

Figure 7.48. Consequences of laboratory evolution of E. coli for 2,000 generations at four fixed temperatures (20°C, 32°C, 37°C, and 42°C) and fluctuating temperatures (daily shifts between 32°C and 42°C). The solid lines connecting the symbols indicate the range of temperatures over which the mean fitness of each group was significantly elevated compared to the common ancestor (Anc). (Figure modified after Mongold et al., 1996.)...

The one-absorption example used for illustration here is appropriate to most van der Waals charge-fluctuation forces because of the important, usually dominant, UV-frequency range of fluctuations. Temperature is not usually a consideration the summation over sampling frequencies can often be smoothed into a continuous integration. However, retardation screening acts in any situation in which separations are more than a mere 20-30 A. Only for distances less than 20 A and, sometimes, for distances greater than 10,000 A, can the van der Waals interaction between parallel-planar surfaces be said to vary by the 1/Z2 power law that it demurely reveals in its simplest representation. 

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