Compressibility, nonisothermal

The residence time of the polymer particles in the reactor and the temperature history experienced by these particles during their journey through the reactor is governed by the compressible nonisothermal Navier-Stokes equations. 

Nonisothermal crystallization Guerra et al. [ 16] reported on sPS/PPE blends of various compositions, prepared by compression molding (T ax = 290°C and Wx = 10 min) and then cooled to room temperature at a rate of 10°C/min. Their DSC results show that, below 50wt%, sPS is completely amorphous. Moreover, WAXD spectra of the same samples indicate that the amount of the a form, which is 100wt% in neat sPS, decreases on increasing PPE and rmax (Figure 20.1a and b) in favor of the (3 form. The authors reported that the loss of the memory of the a form, which they suggested for melt-crystallized neat sPS, is more rapid for the same temperature and time when PPE is present [16]. 

Duff et al. [27] reported a study made by means of DSC and WAXD on SPS/ PPE blends of various compositions, precipitated from ethylbenzene solutions, compression molded at 330 °C for 2 min and then slowly cooled to room temperature. In particular, the WAXD patterns show that in sPS-rich blends (>50 50 wt%) sPS is in a 0 or (3 form, while small amounts of a are present in the 50 50 wt% blend. The kinetics of crystallization and the mechanism of nucleation of sPS were investigated under isothermal and nonisothermal conditions as a function of blend composition and molecular weights of the components. The experimental curves show that the half-time to crystallization, t j2, increases with increasing content and molecular weight of PPE, but is not influenced by the molecular weight of sPS. The crystallization kinetics were... 

Here, u represents a characteristic velocity of the flow and usotmd is the speed of sound in the fluid at the same temperature and pressure. It may be noted that usound for air at room temperature and atmospheric pressure is approximately 300 m/s, whereas the same quantity for liquids such as water at 20°C is approximately 1500 m/s. Thus the motion of liquids will, in practice, rarely ever be influenced by compressibility effects. For nonisothermal systems, the density will vary with the temperature, and this can be quite important because it is the source of buoyancy-driven motions, which are known as natural convection flows. Even in this case, however, it is frequently possible to neglect the variations of density in the continuity equation. We will return to this issue of how to treat the density in nonisothermal flows later in the book. 

We shall see that the sum p(V u) + T E on the right-hand side of (2 52) represents the conversion of kinetic energy to heat, due to the internal friction within the fluid and is known as the viscous dissipation term. The last term on the left-hand side of (2 52) is related to the work required for compressing the fluid. Although this term is identically zero only for constant-pressure conditions (that is, the material is a solid or it is stationary so that Dp jDt = 0), it is frequently small compared with other terms in (2-52) because the density at constant pressure is only weakly dependent on the temperature, and we shall generally adopt this approximation in the analyses of nonisothermal systems in later chapters. 

The volume change in nonisothermal conditions must be corrected for temperature. For non-ideal conditions, the compressibility factor Z is corrected. Thus, Equation 1.13 becomes ... 

For a nonisothermal polytropic compression [where P/pT = constant] of an ideal gas, we can show that... 

Would isothermal or nonisothermal compression with continually increasing temperature be desirable to achieve high-efficiency gas compression Would you want an insulated or cooled compressor ... 

Compression molding is a highly nonisothermal process. In the processing of blanks consisting of a thermoplastic reinforced with long fibers, the blanks are preheated and then placed in the mold, which is at a temperature lower than that of the blanks. In the case of thermoplastic prepregs, the... 

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