Heat effects latent

D. THERMAL EQUILIBRIUM MODEL. The previous ease yields a model that is about as rigorous as one ean reasonably expeet. A final model, not quite as rigorous but usually quite adequate, is one in whieh thermal equihbrium between liquid and vapor is assumed to hold at all times. More simply, the vapor and. liquid temperatures are assumed equal to eaeh other T=T . This eliminates the need for an energy balanee for the vapor phase. It probably works pretty well because the sensible heat of the vapor is usually small compared with latent-heat effects. 

The internal energy changes (sensible-heat effects) can usually be neglected compared with the latent-heat effects. Thus a simple algebraic steadystate energy equation can be used... 

This solution, which corresponds to negligible sensible heat effects, can be used to start the numerical integration for any finite mi, since, in Eq. (99), Uy (0) = 0. The case mi = is well approximated, for example, by the melting of steel originally at room temperature. Here mi = 27, so that latent heat effects play a very small role. Some modification of the transformed variables is necessary to get the equations into convenient form for numerical integration. 

Baxter (B3) uses an enthalpy-flow temperature method, due originally to Dusinberre (D5, D6) and Eyres et al. (E4), whereby the movingboundary effect is reduced to a property variation. To begin with, the melting of a slab of finite thickness initially at the fusion temperature is considered. At the surface of the melt, which is of the same density as the solid, a heat transfer boundary condition is applied. The technique takes into account latent heat effects by allowing the specific heat to become infinite at the fusion temperature in such a way that... 

Latent Heat. Effects in Plumes from Cooling Towers... 

Using an H-x diagram to adjust Eqs, (2,9) and (2,10) for latent heat effects. This approach also converts each component balance line into a curve, but the curve is constructed using an H-x diagram instead of a computer simulation. Further details are described by Fisher (10),... 

Temperature maps (Figure 4, right hand side) require modelling the heat transfer into the 3D snow structure. As mentioned in section 2.1, convection and latent heat effects in snow are negligible for the considered TG (3 K m ). Consequently, the temperature field was computed by considering only conduction effects in both the ice and the pores of the snow... 

The important difference between single-phase and two-phase flows is the interface latent heat effect involved with the latter. Also, in cases with strong curvature effects, surface tension needs to be taken into account. Because of latent heat, the heat transfer rates in two-phase problems are an order of magnitude larger than those in single phase. 

Both first- and second-order transitions are observed in polymers. Melting and allotropic transformations are accompanied by latent-heat effects and are known as first-order transitions. During second-order transitions, changes in properties occur without any latent-heat effects. Below the second-order-transition temperature (glass transition temperature) a rubberlike material acts like a true solid (see Chapter 1). Above this temperature the fixed molecular structure is broken down partially by a combination of thermal expansion and thermal agitation. The glass transition temperature of polystyrene is 100°C below 100°C polystyrene is hard and brittle, and above 100°C it is rubberhke and becomes easily deformed. 

Supercooling can also cause the spontaneous appearance of new phases, accompanied by large latent heat effects and a temporary increase in temperature. Since liquids can be so easily supercooled, cooling curves often fail to locate the solidus reliably cooling curves typically yield values of the solidus temperature that are too low. Therefore, once the liquid phase has completely solidified, the solidus is often determined by reversing the process and heating the solid back to the solidus [20]. To locate... 

The presence of water vapor in the combustion system appears in the latent heat effects and one consequence of high moisture content in coal combustion is that a part of the heat is lost due to evaporation of the moisture in the coal and is not recouped from the combustion products. It is possible that a small amount (5% w/w) of water in the coal may not exert any marked effect on the overall heat requirements, since the sensible heat of the gases vaporizes the water. 

Poly(butylene terephthalate), PBT, is the next member of the homologous series of polyterephthalates with its thermodynamic properties listed in Fig. 6.40. Figine 6.45 presents the crystallinity for a semicrystalline, melt-crystallized PBT sample, calculated with the method of Fig. 4.80, Eq. (3). Below the glass transition, the crystallinity reaches 36.2%. With this crystallinity function, the expected heat capacity without latent heat effects is given in Fig. 6.46. 

Knowledge of the heat capacity of solids and melts is of importance not only for its own sake, but also for the discussion of the various latent heat effects in polymers which occur commonly between the glass transition temperature and the melting point and will be analysed in more detail in Section 4.3. Furthermore, in the glass transition region, the heat capacity may become time dependent without the presence of a latent heat effect. Both of these topics will be discussed in this section. 

In the framework of the thermal effects enumerated in Section 2.5, the increased reversible heat flow rate is due to the latent heat effect (3), which maybe caused by either isolated crystals, which crystallise and melt in a local equilibrium set-up within the network of primary and secondary crystals (5,6) after their rearrangement has ceased (4), or by reversible crystallisation and melting on the lateral surface areas of the crystals (5,6). 

This technique measures heat-related phenomena that are associated with transitions in materials. In this technique the polymer sample is temperature programmed at a controlled rate and, instead of determining weight changes as in TGA, the temperature of the sample is continually monitored. Just as a phase change from ice to water or vice versa is accompanied by a latent heat effect, so when a polymer undergoes a phase change from, for example, crystalline to an amorphous form, heat is either evolved or absorbed. 

More evidence for a critical point comes from adiabatic and nonadiabatic scanning calorimetry measurements [138], [139], a comparison of which yields the latent heat effects associated with a first-order phase transition. Figure 7.19 shows data from both techniques for two chiralities of a CE2 sample. The sharp peaks, which are due to the nonabiatic technique only, represent first-order helical-BPI and BPI-BPIII transitions the BPIII-isotropic peak only shows first-order behavior for X = 0.40. Repeated runs for various chiralities establishes that, for this system, Xc x 0.45. A complete experimental analysis of the rotatory power and calorimetric experiments has been performed by Kutnjak et al. [139], who conclude that the data is consistent with mean field behavior. Since that time, however, new theory has appeared which allows different conclusions. 

If a first-order phase transition occurs between r(0) and T (oo), there will be a nonexponential T(t) variation due to latent heat effects. This situation can be handled [32, 33] by defining a time-dependent heat capacity C(t)=Plt, where P=Pq-(T-Tq)K, . In this procedure it is possible to obtain the latent heat using ... 

Figure 12. The specific heat capacity variation in the N -BP -BP i-I transition region for S.S-MBBPC. The sharp peaks from non-adiabatic scanning through the N -BP] and BP -BPni regions are due to latent heat effects at the first-order transitions. No such effects are seen for the BP -I transition, because this is only a continuous supercritical evolution not a true phase transition in this material [55].

The other class of formulations of the FEM is based on the definition of an effective specific heat. This results in the inclusion of the latent heat effect in the capacitance matrix. There are a number of ways in which this can be provided for. Each of these methods makes use of an enthalpy temperature curve, for example. 

The molar heat capacity at constant pressure, Cp, is defined as the amount of heat, Q, needed to raise the temperature, T, of one mole of substance at constant (atmospheric) pressure by one kelvin in the absence of latent heat effects, such as heats of fusion, crystaUization,... 

It is obvious that the crystallinity degree is not only a result of simulation but also a phenomenon to be kept into account in each step of process modeling, especially, when the latent heat effect of crystallization of the molded object wants to be considered. So the ejqtression of crystallinity is necessary. Many researchers [l,3-5]predict the development of crystallinity by the following Avrami equation ... 

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