Critical temperature difference

As can be seen in the table above, the upper two results for heat transfer coefficients hp between particle and gas are about 10% apart. The lower three results for wall heat transfer coefficients, h in packed beds have a somewhat wider range among themselves. The two groups are not very different if errors internal to the groups are considered. Since the heat transfer area of the particles is many times larger than that at the wall, the critical temperature difference will be at the wall. The significance of this will be shown later in the discussion of thermal sensitivity and stability. 

Pool and Nucleate Boiling—General Correlation for Heat Flux and Critical Temperature Difference... 

Maximum Flux at Critical Temperature Difference for Various Liquids Boiling in Pools Heated by Steam Condensing inside Submerged Tubes... 

Above critical temperature difference for nucleate boiling Vs -in-Vs -in- O.D. (data of correlation)... 

Nucleate boiling is boiling at the tube surfece at a temperature difference between outside tube surface temperature and the fluid body, less than the critical temperature difference. At and beyond the critical temperature difference, metastable and film boiling take place. These produce lower transfer coefficients as the temperature difference increases. 

The nucleate region is the one of interest in most plant design as previously described for plain tube boiling. The critical temperature difference curves have been determined experimentally for a reasonable number of fluids and should be used whenever possible. 

Check to determine that the maximum flux, Q/A, and critical temperature difference. Ah, are not exceeded. 

The nucleate type of boiling is far more common than any other type. This form usually occurs in commercial evaporators, still pots, and similar boiling equipment. Much attention has been given to nucleate boiling and a good many data are available. Because the critical temperature difference is the upper limit to nucleate boiling, it too has received notice. The number of data for it is far from ample, because of the burnout difficulty discussed in Sec. IID. 

It is always desirable to have physical interpretations of unusual phenomena. The existence of a critical temperature difference for nucleate boiling has challenged many thinkers. The easiest explanation occurs... 

The usual correlations proposed for the critical temperature difference or for the maximum heat flux do not specify the metal (B5, R12). Obviously this contributes to the observed deviations between the cor. relations and experimental data. Castle s table above indicates how great the deviations may be. 

The maximum heat flux and the critical-temperature difference are functions of pressure also. Figure 33 shows the data of Cichelli and... 

CURIE POINT (or Curie Temperature). Ferromagnetic materials lose their permanent or spontaneous magnetization above a critical temperature (different for different substances). This critical temperature is called the Curie point. Similarly, ferroelectric materials lose their spontaneous polarization above a critical temperature. For some such materials, this lemperaLure is called the "upper Curie point." for there is also a "lower Curie point." below which the ferroelectric property disappears. See also Ferromagnetism. 

It should be emphasized that the comparatively large change obtained in more recent work is mainly caused by the application of finite-size scaling. Under these circumstances, one certainly needs to reconsider how far the results of analytical theories, which are basically mean-field theories, should be compared with data that encompass long-range fluctuations. For the van der Waals fluid the mean-field and Ising critical temperatures differ markedly [249]. In fact, an overestimate of Tc is expected for theories that neglect nonclassical critical fluctuations. Because of the asymmetry of the coexistence curve this overestimate may be correlated with a substantial underestimate of the critical density. 

Both equations are verified simultaneously for the critical temperature difference E... 

Compared with the heat release rate by a reaction, which follows Arrhenius law, one obtains the Semenov diagram (Figure 2.6). From this diagram, we can calculate the critical temperature difference (Equations 2.32-2.34). But this also calculates the critical heat release rate as a function of q0 ... 

The properties of the Nicalon /SiC (PIP) system followed a similar pattern (A/c(ou) = 400°C, A rc(omc) = 500°C), though this system failed through an interlaminar shear failure process (delamination) and the property reduction saturated at A T= 600°C. The Nicalon /SiC (CVI) system failed by fracture through fibre planes but its properties (ou, omc, WOF) had the same critical temperature difference, A Tc = 700°C. The pre- and post-quench stress-displacement curves for this material can be seen in Fig. 15.9. However, measurement of the Young s modulus of this system before and after quenching by means of a dynamic mechanical resonance technique showed the onset of decrease at ATC(E) = 400°C, i.e. significantly lower than the A 7C of the other properties. 

One of the best-known physical ordering phenomena is the Benard cells, which occur during the heating a fluid held between two parallel horizontal plates separated by a small distance. The lower plate is heated, and the temperature is controlled. The upper plate is kept at a constant temperature. When the temperature difference between the two plates reaches a certain critical value, the elevating effect of expansion predominates, and the fluid starts to move in a structured way the fluid is divided into horizontal cylindrical convection cells, in which the fluid rotates in a vertical plane. At the lower hot plate, the hot fluid rises later, it is cooled at the upper plate, and its density increases again this induces a movement downward, as seen in Figure 13.2. The Benard cells are one of the best-known physical examples of spontaneous structurization as a result of sufficient distance from equilibrium, which is the large temperature difference between the plates. The critical temperature difference ( A 7 )c can be determined from the... 

If this AT is exceeded, transition to the upper steady state will occur. For many industrial reactions E/RT is typically between 16 and 24, and the reaction temperatures may be 300 to 500 K. Consequently, this critical temperature difference Ar wiU be somewhere around 15 to 30°C. 

Abrupt cooling will induce tensile stress in the glass surface, given for a plate by relationship (54) on p. 164, where Ta To (Tq is the initial temperature) and T is the cooling medium temperature. The critical temperature difference AT (Tq — T) is then given by equation... 

This chapter concludes the review on Boiling of Liquids, the first part of which, published in Volume I of Advances in Chemical Engineering, 1956, included I. Introduction II. Nucleate Boiling and the Critical Temperature Difference. 

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