Center-line temperatures

As the thickness of the laminate increases, the strength of this thermal spike and the degree of thermal lag during heat-up increases. Figure 8.8 shows the results for a 62.5-mm (500 ply) laminate of the same material. Now the center-line temperature never reaches the autoclave temperature during the first dwell, and the thermal spike during the second dwell is nearly 135°C. The thermal spike is directly related to the release of internal heat during cure. The thermal lag is a manifestation of the low thermal diffusivity of polymer matrix composites. 

Figure 5.24 Center-line temperature history during heating of a finite thickness plate. Note that cooling is represented by the same curve using 1 — as the dimensionless temperature.

Figure 5.25 Experimental and computed center-line temperature history during heating of an 8 mm thick PMMA plate. The initial temperature To=20°C and the heater temperature Ts=140°C. [7]...

Figure 5.26 Center-line temperature histories of finite thickness plates during convective heating for various Biot numbers.

The center-line temperature for plates of finite thickness is given in Fig. 5.26 and a comparison between the prediction and experiments for an 8 mm thick PMMA plate cooled with a heat transfer coefficient, h, of 33 W/m2/K is given in Fig. 5.27. As can be seen, theory and experiment are in relatively good agreement. 

Evolution of the center line temperature for a constant Cp thermoplastic. 

Figure 8.26 Evolution of the center-line temperature for a cooling semi-crystalline plate with variable CP(T).

Implicit schemes are unconditionally stable, this is shown in Fig. 8.27 where the evolution of the temperature, in a/ag steps, for values of a/ag higher than 0.5 is shown. Higher values of a/ag mean that we can use higher At, which at the end implies lower computational cost and faster solutions. The results in Fig 8.27 were obtained with the fully implicit Euler scheme, i.e., to = 1. The comparison between the implicit Euler and the Crank-Nicholson, to = 0.5 is illustrated in Fig. 8.28 for the center line temperature evolution. Although there is no apparent significance difference, we expect that the CN scheme is more accurate due to its second order nature. 

From this equation it follows that the center line temperature, TCt is given by ... 

Now, in fully developed flow it is usually convenient to utilize the mean fluid temperature, Tmt rather than the center line temperature in defining the Nusselt number. This mean or bulk temperature is given, its explained in Chapter 1, by ... 

The variations of Nuq, Nuom, and the dimensionless center line temperature, dc, with Z given by this program are shown in Fig. 4.18. 

Nusselt number and center line temperature variation in developing flow in a pipe with a uniform wall temperature. 

The computer program DEVPIPE discussed above allows either a uniform wall heat flux or a uniform wall temperature to be considered. The variations of Nud, Nuomi and the dimensionless center line temperature, 6, with Z given by this program for the uniform wall heat flux case are shown in Fig. 4.19. 

FIGURE SJ9 (Comparison of furnace temperature to center-line temperature of a cylindrical Ca(X)3 sample thrust into a preheated oven. Taken from Satterfield andFeales [15]. 

Temperature Rise in Heating Wire. A current of 250 A is passing through a stainless steel wire having a diameter of 5.08 mm. The wire is 2.44 m long and has a resistance of 0.0843 Cl. The outer surface is held constant at 427.6 K. The thermal conductivity is fc = 22.5 W/m K. Calculate the center-line temperature at steady state. 

The center line temperature of the fuel was measured by thermocouples during irradiation. The following facts were noted ... 

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