Profile heat flux

All the references to burn-out have thus far been concerned with uniformly heated channels, apart from some of the rod bundles where the heat flux varies from one rod to another, but which respond to analysis in terms of the average heat flux. In a nuclear-reactor situation, however, the heat flux varies along the length of a channel, and to find what effect this may have, some burn-out experiments on round tubes and annuli have been done using, for example, symmetrical or skewed-cosine axial heat-flux profiles. Tests with axial non-uniform heating in a rod bundle have not yet been reported. 

This is derived by substituting from the heat-balance expression, Eq. (20). Now, the skewed-cosine heat-flux profile being considered gives a known functional relationship between the flux and the quality at any position along the channel. By equating this relationship with Eq. (35), a solution can be obtained giving the local values of (j> and k at the predicted burn-out position. The corresponding peak flux can then be evaluated, and in this way the predicted burn-out lines for the three mass velocities in Fig. 40 can be drawn. 

Fig. 40. Test of the Barnett local-conditions hypothesis applied to a tube with a skewed-cosine heat-flux profile [from Barnett (B4)]. Fluid water, d = 0.422 in., L — 12 in., P = 2000 psia.

Y = axial heat flux profile parameter Y = subchannel imbalance factor... 

Axial heat flux parameter Y The parameter Y, which replaces the heat flux shape factor in the CHF correlation, is not only a measure of the nonuniformity of the axial heat flux profile but also a means of converting from the inlet subcooling (AHin) to the local quality, X, form of the correlation via the heat balance equation. It is defined as... 

An approximate value of Yx at Z = Z, may be calculated by summing over a number of intervals of length. Thus, for a continuous axial heat flux profile, Yt is given by... 

FIGURE 14.6 Radiant heat flux profile in the LIFT. 

The gas flow to the radiant panel is set to obtain a heat flux at the 50 mm location that is 5-10kW/m2 above the critical heat flux for ignition (Section 14.3.2.3.2). The heat flux is verified with a heat flux meter inserted into a calcium silicate dummy specimen. The heat flux profile is shown in Figure 14.6 and can be used to determine the incident radiant heat flux at any location along the specimen center-line. The flux invariant may vary slightly and is usually determined for each apparatus during the initial calibration. 

Bottom-fired furnaces are not very common in modern ammonia plants. They have a rather constant heat flux profile along the tube with high metal temperatures on the outlet side. Examples are the Exxon reformer and the old Chemico round furnaces. 

Two problems (a) maximization of hydrogen and export steam flow rate, and (b) maximization of hydrogen and export steam flow rate, and minimization of total heat duty of the reformer. Oh et at. (2001) considered heat flux profile as a decision variable instead of furnace gas temperature in Rajesh et at. (2001). Oh et al. (2002b) optimized an indusUial hydrogen plant based on refinery off-gas. Oh a/.(2001) Oh /. (2002b)... 

Heat flux versus heat release for a typical burner used in ethylene furnaces. (From Colannino, Mathematical Models for Characterizing and Predicting Heat Flux Profiles from Ethylene Cracking Units, Proceedings of the 2007 AlChE Spring National Meeting, Houston, TX, April 23-26,2007.)... 

Effect of fuel composition on measured heat flux profiles in a furnace for a burner firing at 3.5 x 10 Btu/hr. (From Hayes, R., Singh, R, Foote, D., and Baukal, C. E., Heat Flux from Process Burners, Proceedings of the ASME IMECE, New York, November 11-16, 2001, Heat Transfer Division, Vol. 369, No. 4, pp. 161-64,2001.)... 

Furnace cooling and temperature control are important for a number of reasons. A process burner test can be compromised by operating at temperatures significantly higher or lower than the design temperature specified by the client. A correct firebox outlet temperature is essential for an accurate prediction of the heat flux profile. Temperatures that are too low can negatively impact burner stability or overpredict CO production. Firebox temperatures that are too high could lead to excessive NO, production. 

Since the heat transferred to the furnace tubes is the desired information, the heat flux probe is placed in the same plane as the hot face of the tubes. The heat flux is measured opposite the fired wall via access ports along the vertical axis of the furnace (Figure 18.19). Once the data is collected, it is plotted on a curve and compared to the desired heat flux profile. 

Figure 13 Optimal control of methane conversion to ethylene and acetylene (a) optimal Chflux profile (b) optimal heat flux profile (c) mass fraction profiles at optimal conditions (d) temperature profile at optimal conditions... 

The following heat flux profile was generated from independent simulations of the heat transfer in the firebox. First tube 23 kcal/m s (96 kJ/m s) second tube 20 (84) third tube 19 (80) fourth tube 17 (71) fifth tube 15 (63) sixth, seventh, eighth, ninth, and tenth tubes, 14 (59). With this heat flux profile, the conversion, temperature and total pressure profile of Fig. 2 was obtained. The agreement with the industrial data is really excellent. Also, the product distribution is in complete agreement as can be seen from Fig. 3 the simulated yields for ethylene, hydrogen, and methane, for example, are, respectively, 47.92, 3.79, and 3.49 the... 

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