Thermal entry

TDI isomers, 210 Tear strength tests, 242-243 TEDA. See Triethylene diamine (TEDA) Telechelic oligomers, 456, 457 copolymerization of, 453-454 Telechelics, from polybutadiene, 456-459 TEM technique, 163-164 Temperature, polyamide shear modulus and, 138. See also /3-transition temperature (7)>) Brill temperature Deblocking temperatures //-transition temperature (Ty) Glass transition temperature (7) ) Heat deflection temperature (HDT) Heat distortion temperature (HDT) High-temperature entries Low-temperature entries Melting temperature (Fm) Modulu s - temperature relationship Thermal entries Tensile strength, 3, 242 TEOS. See Tetraethoxysilane (TEOS)... 

The thermal entry length should be considered by comparison between experimental and numerical results. 

The entry rate was calculated using radical generation rate, thermal entry rate, reentry rate, and initiator efficiency. The method for calculating initiator efficiency will be discussed later. 

To overcome thermal entry effects, the segments may be virtually stacked with the outlet conditions from one segment that becomes the inlet conditions for the next downstream section. In this approach, axial conduction cannot be included, as there is no mechanism for energy to transport from a downstream section back to an upstream section. Thus, this method is limited to reasonably high flow rates for which axial conduction is negligible compared to the convective flow of enthalpy. At the industrial flow rates simulated, it is a common practice to neglect axial conduction entirely. The objective, however, is not to simulate a longer section of bed, but to provide a developed inlet temperature profile to the test section. 

Temperature(s). See also Blackbody temperature sensor Cure temperature Curie temperature Eutectic temperature Fictive temperature Furnace temperature Glass- transition temperatures Heat entries Heating Hot entries Refrigeration Target temperature emperature measurement Thermal entries Thermo-entries Transition temperatures in analysis of water, 26 35 biofiltration system, 10 76 in biological wastewater treatment,... 

The ene reaction is strongly catalyzed by Lewis acids such as aluminum chloride and diethylaluminum chloride204 Coordination by the aluminum at the carbonyl group increases the electrophihcity of the conjugated system and allows reaction to occur below room temperature, as illustrated in Entry 6. Intramolecular ene reactions can be carried out under either thermal (Entry 3) or catalyzed (Entry 7) conditions 205 Formaldehyde in acidic solution can form allylic alcohols, as in entry 1. Other carbonyl ene reactions are carried out with Lewis acid catalysts. Aromatic aldehydes and acrolein undergo the ene reaction with activated alkenes such as enol ethers in the presence of Yb(fod)3 206 Sc(03SCF3)3 has also been used to catalyze ene reactions.207... 

The Graetz problem considers the thermal entry of an incompressible fluid in a circular pipe with a fixed velocity profile. The situation is illustrated in Fig. 4.16. The Graetz problem is a classic problem in fluid mechanics, and one that permits an analytic solution. After some hydrodynamic entry length, the velocity profile approaches a steady profile that is,... 

Fig. 4.16 Illustration of the Graetz problem. A fully developed parabolic velocity profile is established in a circular duct and remains unchanged over the length of the duct. There is a sudden jump in the wall temperature, and the fluid temperature is initially uniform at the upstream wall temperature. The thermal-entry problem is to determine the behavior of the temperature profile as it changes to be uniform at the downstream wall temperature. Because the flow is incompressible, the velocity distribution does not depend on the varying temperatures.

Fig. 4.17 Nondimensional temperature profiles (left-hand panel) in the thermal entry of a circular duct with a fully developed velocity profile. The profiles are shown at various nondimensional downstream locations z. Also shown is the nondimensional heat-transfer coefficient, Nu as a function of the nondimensional downstream position.

The Circular Tube Thermal-Entry-Length, with Hydrodynamically Fully Developed Laminar Flow... 

Figure 8.4 Sketch for the thermal-entry length problem.

Table 8.1 Infinite-series solution functions for the circular tube constant surface temperature thermal-entry length.

Figure 8.5 Development of the temperature profile in the thermal-entry region of a pipe.

Azer, N.Z., Thermal Entry Length for Turbulent Row of Liquid Metals in Pipes with Constant Wall Heat Rux , Trans. ASME Serv. C, J. Heat Transfer, Vol. 90. pp. 483-485, 1968. 

We start this chapter with a general physical description of internal flow, and the average velocity and average temperature. We continue with the discussion of the hydrodynamic, and thermal entry lengths, developing flow, and fully developed flow. We then obtain the velocity and temperature profiles for fully developed laminar flow, and develop relations for the friction factor and Nusselt nmnber. Hinally we present empirical relations for developing and full developed flows, and demonstrate their use. 

B Have a visual understanding of different flow regions in internal flow, such as Ihe entry and the fully developed flow regions, and calculate hydrodynamic and thermal entry lengths,... 

Th regioii of flow over which the thermal boundary layer develops and re.iches (he tube center i.s called the thermal entrance region, and the length of this region is called the thermal entry length L,. Flow in the thermal... 

During laminar flow in a tube, the magnitude of the dimensionless Prandtl number Pr is a measure of the relative growth of the velocity and thermal boundary layers. For fluids with Pr = I, such as gases, the two boundary layers essentially coincide with each other. For fluids with Pr > I, such as oils, the velocity boundary layer outgrows the thermal boundary layer. As a result, the hydrodynamic entry length is smaller than the thermal entry length. The opposite is tnie for fluids with Pr < 1 such as liquid metals. 

The hydrodynamic entry length is usually taken to be the distance from the lube entrance where the wall shear. stress (and thus the fficliou factor) reaches within about 2 percent of the fully developed value. In laminar flow, the hydrodynamic and thermal entry lengths are given approximately as (see Kays and Crawford (1993) and Shah and Bhatli (1987)]... 

In turbulent flow, the intense iqjxing during random fluctuations usually overshadows the effects of molecular diffusion, and therefore the hydrodynamic and thermal entry lengths ate of about the same size and independent of the PflLndil number. The hydrodynamic entry length for turbulent flow can be detennined from [see Bbatti and Shah (1987) and 7.hi-qing (1982)]... 

The entry length is much shorter in turbulent flow, as expected, and its dependence on the Reynolds number is weaker. In many lube flotvs of practical interest, the entrance effects become insignificant beyond a tube length of 10 diameters, and the hydrodynamic and thermal entry lengths are approximately taken to be... 

C How is the thermal entry length defined for flow in a tube In what region is the flow in a tube fully developed ... 

S-18C Consider the flow of mercury (a liquid meial) in a tube. How will the hydrodynamic and thermal entry lengths compare if the flow is laminar How would they compare if (he flow uere turbulent ... 

The unusual behavior of Nu decreasing with increasing Re in the laminar regime in microchannels may alter the status of thermal development and hence the conventional thermal entry length, since the variation of the heat transfer coefficient along the flow is a variation of the boundary condition. 

The effect of any variation of the boundary condition on thermal entry length has not been explained. 

The thermal entry flow with fully developed velocity profile... 

Laminar flow that is developing hydrodynamically or thermally, (entry flow) constant wall temperature ... 

Chang, M. W., Finlayson, B. A., On the proper boundary condition for the thermal entry problem. Int. J. Numer. Meth. Engng. 1980 15, 935-942. 

The entrance length z/d for a fully developed velocity profile, for a concentration profile, or for a corresponding thermal entry length are given as 0.05 Re, 0.05 Re Sc, 0.05 Re Pr, respectively. The symbols are summarized in Table 11. 

C. J. Hsu, An Exact Analysis of Low Peclet Number Thermal Entry Region Heat Transfer in Transversely Nonuniform Velocity Fields, AIChEJ., (17) 732-740,1971. 

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