Temperature amplitudes

The previous subsection described single-experiment perturbations by J-jumps or P-jumps. By contrast, sound and ultrasound may be used to induce small periodic perturbations of an equilibrium system that are equivalent to periodic pressure and temperature changes. A temperature amplitude 0.002 K and a pressure amplitude 5 P ss 30 mbar are typical in experiments with high-frequency ultrasound. Fignre B2.5.4 illustrates the situation for different rates of chemical relaxation with the angular frequency of the sound wave... 

Fig. 6.38 Time variation of fluid temperature at the outlet manifold q = 200 kW/m (a) temperature fluctuations, (b) temperature amplitude spectrum. Reprinted from Hetsroni et al. (2006b) with permission...

Both water temperature and PCE concentration show a clear annual variation. The maximum (minimum) water temperature is registered in the first well about 18 days earlier than in the second one, and the temperature amplitudes are approximately equal in both wells. In contrast, the time lag observed for the concentration variation of PCE between the two wells is 6 months. The concentration amplitude of PCE in the downstream well, that is, the difference between maximum and mean concentration, is only about 65% of the amplitude in the upstream well, but the annual mean concentrations are equal in both wells. 

Direct experimental proof of the possibility of rapid gas ignition under compression by a shock wave was given by Leipunskii and the author. Compression by the shock wave was accomplished by shooting a fast bullet from a special small-caliber rifle into the explosive mixture. In front of the body, which was flying with supersonic velocity, a steady shock wave formed whose velocity with respect to the gas was equal to the velocity of the body. This condition determined the pressure and temperature amplitudes in the wave. The duration of the compressed state of the gas did not exceed 10"5 sec. For a bullet velocity of 1700-2000 m/sec, ignition of the mixture 2H2 + 02 + 5Ar was observed. 

Figure 7-14. Simulated annual variation in soil temperatures, showing a decreasing amplitude with depth and a seasonal shift of the maximum. The vertical arrows indicate the temperature amplitude at the specified depths in the soil. The average daily temperature at the soil surface was assumed to vary sinusoidally, with a maximum on August 1 and an annual amplitude of 10°C the damping depth d is 1.7 m.

The second microscale heat transfer issue considered in this paper deals with short time scales and their influence on the dimensions required for good heat transfer. Many cryocoolers use oscillating flows and pressures with frequencies as high as about 70 Hz. Heat flow at such high frequencies can penetrate a medium only short distances, known as the thermal penetration depth temperature amplitude of a thermal wave decays as it travels within a medium. The distance at which the amplitude is 1/e of that at the surface is the thermal penetration depth, which is given by... 

Volume-phase grating Population (species)-phase grating Density-amplitude grating Temperature-amplitude grating Volume-amplitude grating Population (species)-amplitude grating... 

Ni wire (Fig. 7). The temperature amplitude 6 in water was 1.25 K. The minimum sample volume for Eq. (10) to apply is that of a liquid cylinder centered on the wire and having a radius equal to about 3//. At 2/= 1 Hz, this amounts to 25 pi. The method was validated with pure fluids (water, methanol, ethanol and ethylene glycol), yielding accurate A -ratios within 2% (Eq. 11) and absolute a value for water within 1.5% (Eq. 12). 

Rectal temperature Amplitude possibly related Minors and... 

As for the modulus in DMA, which is the ratio of peak stress to peak strain, Q is proportional to the ratio of peak heat flow to peak temperature-amplitude (multiplied with the square-root expression) and equals the reversing Cp [see Equation (4)]. 

This means that a strain wave is accompanied by a temperature wave. With /2 100, e 10 and T=1K, this leads to a temperature amplitude AT 10 mK that should be detectable. The resulting temperature gradient VT can also be of importance for ultrasonic attenuation effects (Muller et al. 1986). 

Merzlyakov M, Wurm A, Zorzut M, Schick C (1999) Frequaicy and Temperature Amplitude Dependence of Complex Heat Capacity in the Melting Region of Polymers, J Macromolecular Sci, Phys 38 1045-1054. 

Large modulation temperature amplitudes ( 1.5-3 K) should be used when measuring weak glass transitions. Smaller amplitudes are recommended for sharp transitions which are only a few degrees wide. Finally, avoid amplitudes smaller than 0.03 K as they are difficult to control. Note that large modulation temperature amplitudes and short periods require a considerable sample... 

Figure 4.27 illustrates in its top sketch the simple sawtooth modulation, discussed in Section 3.1, and the response to a sawtooth modulation is shown in Figure 4.17. The amplitudes of the Fourier series of the sawtooth modulation decrease with 1/r, so that the precision of the analysis of higher harmonics decreases rapidly. To overcome this difficulty, the complex sawtooth shown in the center sketch of Figure 4.27, as well as given by the series of Eq. (15), was proposed [45]. Its first four Fourier terms describe practically all the variation shown in Figure 4.17. An overall modulation repeat of 210 s yields almost equal temperature amplitudes with periods of 210, 70, 42 and 23.3 s.

A similarly useful complex modulation is the meander modulation at the bottom of Figure 4.27. In this case, the temperature amplitudes of the Fourier series decrease linearly with the order of the harmonics, but the derivative A AjJAt = Aj X T which actually enters into Eq. (10) is constant. This method is particularly easy to program for any standard DSC. 

Figure 4.85. Lissajous figures of the runs at 315.6 K with different modulation-temperature amplitudes, as seen in Figure 4.84, showing melting and crystallisation at the larger amplitudes.

The numbers indicate thickness of PODMA lamellae or diameter of PODMA cylinders estimated based on i oDMA values from NMR. Peak maxima from scans with rates of dT/At = 10 K/min. Dynamic glass temperatures from c -maxima in TMDSC scans (time period tp = 60s, temperature amplitude Ta=0.4K, underlying heating rate - -2 K/min). Taken from scans with rates of 10 K/min ( 1 K/min). Taken from Avrami plots (Fig. 12.12). The uncertainty is about 0.2. The width of the transformation interval can be estimated from Alogtc = 1.253/n (cf. [37]). 

FIGURE 9 Seasonal climatology of planetary wave temperature amplitude (K) at 50 mb ( 21 km). Note the large amplitudes throughout Northern Hemisphere winter. In the Southern Hemisphere, wave amplitudes remain relatively small until late winter. [Data courtesy of W. Randel, National Center for Atmospheric Research.]... 

Fig. 5 and 6 show curves of equal a-values for e = 0.02075 and B = 15 and B = 30. These diagrams illustrate that small temperature amplitudes are restricted to a very small zone near the borderline a = o. All analytical approximations must fail in the main part of the region a > o, B > o where the a-values are very near to 1. 

To our own surprise a comparatively simple semi-empirical approximation works quite well in the range of high temperature amplitudes. From Eq. (1) a coupling equation can be obtained by elimination the dimensionless reaction rate... 

Figure 5. Stability diagram with curves of equal temperature amplitude (B = 15,( = 0,02075)...

From several numerical calculations we found that the oscillations of Y are considerably smaller than those of v. This effect is demonstrated for a typical limit cycle with a high temperature amplitude in Fig. 7. 

The Figures 9 and 10 show a comparison of the experimental data of the oscillation period and the temperature amplitude with the computed results. The basis of these plots is a refined mathematical model that takes the evaporation of water into account. 

If the temperature amplitude in a dimensionless presentation, of any distance x from the cavity surface, via the quotient position of the probe is applied to the temperature oscillation/l, a universal context results, out of which the position of the temperature sensor can be determined at a desired temperature amplitude (Figure 2.107). 

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