Latent heat release

In this description the temperature field has been taken to be linear in the coordinate y and to be independent of the shape of the melt/crystal interface. This is a good assumption for systems with equal thermal conductivities in melt and crystal and negligible convective heat transport and latent heat release. Extensions of the model that include determination of the temperature field are discussed in the original analysis of Mullins and Sekerka (17) and in other papers (18,19). 

The heat balance follows a similar relationship with the rate of latent heat release in proportion with the amount of element crystallized... 

The way in jvhich the condensate forms on the surface, i.e., in the form of a continuous film or in the form of discrete droplets, has a strong influence on the heat transfer rate. In film condensation, the latent heat released by the vapor must be... 

Because sensible heat effects are being neglected, the rate of latent heat release by the condensing vapor can be equated to heat transfer rate through the film to the wall, i.e., considering the control volume of length dx ... 

The Jakob number is basically a measure of the importance of subcooling expressing, as it does, the change in the sensible heat per unit mass of condensed liquid in the film relative to the enthalpy associated with the phase change. The Jakob number is small for many problems, i.e the sensible heat change across the liquid film is small compared to the latent heat release. For example, for cases involving the condensation of steam, Ja, is typically of the order of 0.01. 

The effect of subcooling in the film will next be considered. As indicated previously, the sensible heat transfer associated with the subcooling of the liquid film is often small compared to the latent heat release and has been neglected in the above analysis. However, for working fluids with low values of latent heat, such as most refrigerants, a correction to the above analysis to account for subcooling may sometimes be needed. 

Three different isothermal crystallization experiments were performed in this work classical static (i.e., quiescent) crystallization in the DSC apparatus, dynamic crystallization with the apparatus described above, and dynamic-static crystallization. Dynamic isothermal crystallization consisted in completely solidifying cocoa butter under a shear in the Couette apparatus. Comparison of shear effect with results from literature was done using the average shear rate y. This experiment did not allow direct measurement of the solid content in the sample. However, characteristic times of crystallization were estimated. The corresponded visually to the cloud point and to an increase of the cocoa butter temperature 1 t) due to latent heat release. The finish time, was evaluated from the temperature evolution in cocoa butter. At tp the temperature Tit) suddenly increases sharply because of the apparition of a coherent crystalline structure in cocoa butter. This induces a loss of contact with the outer wall and a sharp decrease in the heat extraction. 

Following the notation of Chap. 2, we denote the latent heat released per unit mass Hl — Hs as L. Then, because u in the solid phase is zero, condition (2-121a) can be written in the form... 

Migrating tides are those waves which propagate westward with the apparent motion of the Sun. They have significant diurnal and semi-diurnal components. Non-migrating tidal components are also harmonics of the solar day, but they may be stationary, or propagate either eastward or westward. Their dominant source is provided by latent heat release in the troposphere, and thus related to meteorological processes in the lower atmosphere. A small semi-diurnal tide is also forced by the gravitational attraction of the Moon. 

The latent heat of evaporation of water per gram A// is a weak function of temperature and is 2.5 kJ g l at 0°C and 2.25 kJg-1 at 100°C. imw is the mass of water vapor in the air parcel, then the latent heat released for the infinitesimal motion of the air parcel will be equal to — AHv dmw. This term needs to be added to the RHS of the parcel energy balance given by (16.2) ... 

The latent heat release during cloud formation makes clouds warmer than the surrounding cloud-free air. This higher temperature enhances the buoyancy of clouds, as will have been noticed by anyone who has flown through clouds in an airplane. 

The latent heat release/absorption during phase change is determined by the local phase change rate ... 

Batch melting model including latent heat release... 

A simple schematic explanation of the above can be seen in Fig. 4, where the heat-capacity profiles of the two modes of operation are shown in the case of a first-order transition. The integral of the gray-shaded part corresponds to the amount of latent heat released. Note that in the case of a second-order transition (L = 0) one obtains identical Cp and Cp eff profiles. In Figs. 5 and 6, the resolutiOTi of the relaxation runs is somewhat smaller than that of the ac runs. Nevertheless, they are very important when a precise determination of the latent heat is an issue. The following section shows some examples of the heat-capacity response near the critical point for LCs and LCEs. 

Firm evidence for such a picture is the pronounced NMR line broadening observed at the PN-N transition, indicating a broad spread of the order parameter values (Figs. 1 lb and 12). Moreover, the phase transition region is also distinguished by a nmizero latent heat, released over a broad temperature interval (Fig. 5b). 

Unlike the first two scenarios, where the parameters were set by fitting tmly the experimental My i(T) data, for the mixed scenario the fit was made simultaneously for both the My i(T) and My T) datasets. In this way, the relative values of the parameters were determined with relatively high precision (the typical maximum error for any parameter among a, B, C, or G for the displayed fit is about 15%). Actually, since these parameters are not independent, only the relative values (ratios) of these parameters can be determined from the H-NMR data, e.g. G/Gc-Their absolute values are accessed from an additional calorimetric measurement, e.g. a measurement of the latent heat released at the phase transition. 

Figure 18 Comparison between the experimental and simulated evolutions of the latent heat released in the DSC pan of a cocoa butter sample cooled at a constant cooling rate. (From Ref. 50.)...

The sample was initially in a completely liquid state at 37°C. A cooling rate between 0.5 and 4°C/min was chosen. Figure 18 presents the experimental and simulated evolution of the latent heat released by the sample for the four different cooling rates smdied. As forecasted, a mixture of phases II and III was formed. Simulated results were similar to the experimental ones. Simulated curves were interrupted before the end of the crystallization, because calculation stopped when the sample reached 14°C. As a matter of fact, below this temperature, experimental measurements could not be obtained because crystallization kinetics was too fast and crystallization started before the isothermal temperatiue was reached. The slight bump in the experimental curves at slow cooling rates, which is aiso reproduced in the simulated curves, corresponds to a stop in crystallization between 17 and 16°C, because the maximal fraction of solid that can form does not change between these two temperatures. 

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