Nonuniform heating

Nonuniform heat flux of die radiant seetion of furnaee. 

One result of nonuniform heating is that burn-out does not always occur at the channel outlet as it does with uniform heating, provided instabilities are avoided and the flow is vertically upwards. Consequently, the problem of analysis is made that much more difficult. The obvious first step is to see if... 

No really effective way has yet been found for predicting burn-out in nonuniformly heated channels, but there is one method that does appear consistently to get within about +20%. The method was first demonstrated... 

Stevens, G. F., Elliott, D. F., and Wood, R. W., An experimental comparison between forced convection burnout in freon-12 flowing vertically upwards through uniformly and nonuniformly heated round rubes, AEEW-R426, H. M. Stationery Office, London (1965). 

The critical pressure, pc, for water is 3,206 psia (22 MPa). The product of constants CaC is 0.23, which was evaluated from existing water DNB data for circular tubes. As Eq. (5-20) was developed from a uniform heat flux distribution, a shape factor Fc (Tong et al., 1966a) should be applied to the correlation in a case with nonuniform heat flux distribution. 

This solution is readily extended to the case of a nonuniform heat flux distribution for Eq. (5-24) ... 

Because the components of the analytical expression for C are not sufficiently known to permit an analytical evaluation, C is determined empirically as a function of the local quality at the point of DNB, XDNB, (under nonuniform heat flux conditions) and the bulk mass flux, G. The empirically determined expression for C is... 

Weisman and Pei applied their approach to data from tubes with nonuniform axial heat flux. They found the predictive scheme to hold without the need for any nonuniform heat flux correction factor. The accuracy of their prediction was only slightly less than that of the W-3 correlation, Eq. (5-106), for the data they examined. 

For a midchannel dryout in a nonuniform heat flux distribution, GD > 0 in both upstream and downstream regions of the dryout, and at the dryout GD = 0 and (dGJdz) = 0. The wall in the downstream region of the dryout is wetted it follows, then, that d2Eldz2 > 0. Equation (5-64) becomes... 

Correlations for CHF in refrigerants Weisman and Pei (1983) suggested a theoretically based predictive procedure for CHF at high-velocity water flow in both uniformly and nonuniformly heated tubes, which was found to yield equally good results with experimental data for four other fluids R-l 1, R-113, liquid nitrogen, and anhydrous ammonia. 

For a nonuniform heat flux distribution, the energy equation of the test section becomes... 

In the quality flow region, where the CHF occurs at the exit of the channel, experimental results indicate that the critical power of a nonuniformly heated test section is a function of Hin, L, De, G, and p, and suggest that an approximate relationship for boiling crisis in an axially nonuniformly heated test section can be written as... 

In the subcooled or low-quality region, the boiling crisis of a nonuniformly heated section can occur upstream of a boiling channel. The equation for predicting the local CHF can be written as... 

The dryout heat flux from a uniform heat flux distribution can be correlated as a function of p, X, and (DU2G) but is not generally valid for a nonuniform heat flux distribution. 

DNB,non = axial location at which DNB occurs for nonuniform heat flux (in.),... 

Predictions of a nonuniform heat flux, DNB non obtained by using <7dNB(W.3), f°r uniform heat flux in a single tube and the shape factor, Fc, agree very well with the measured nonuniform flux condition, DNB non of Biancone et al. (1965), Judd et al. (1965), and Lee and Obertelli (1963), as shown in Figure 5.70. 

The nonuniform heat flux prediction of W-3 DNB correlation (developed from single channel data as shown in Fig. 5.70) was verified in axially, nonuniformly heated bundles by comparison of the 284 DNB data points (Fig. 5.72) with the W-3 correlation through a subchannel analysis including spacer factor, showing excellent agreement. The standard deviation was 7.4%. 

Correlation for nonuniform heat flux. On the basis of Tong s shape factor formulation (1967a), Wilson et al. (1969) developed another set of constants ... 

For a cluster with uniform axial heat flux, Y = 1 at all Z. For nonuniform heat flux, Y varies along the length. For example, with a chopped-cosine profile, Y < 1 over the first part of the channel, Y = 1 at about two-thirds of the length, and Y > 1 near the exit of the channel. 

Correlation for nonuniform axial heat flux Two methods of correlating nonuniform heat flux have been postulated ... 

Local quality method Dryout occurs when the local nonuniform heat flux equals the uniform heat flux dryout value at the same local conditions (quality, etc.). 

Total power method The dryout power of a nonuniformly heated channel is the same as if the channel were heated uniformly. 

For nonuniform heat flux the first postulate states that the local quality, X, is the same, and the CHF may be written, via the heat balance containing Y, as... 

Extension of A.R.S. CHF correlation to nonuniform heating. To extend the correlation described in the previous section, the saturation boiling length hypothesis is followed. By means of a straightforward transformation, Eq. (5-133) becomes... 

Table 5.17 Comparison of ARS correlation with experimental data for nonuniform heating... 

Bypass ratio of parallel channels Mass flux and power Nonuniform heat flux... 

Synthetic chemists desire well defined reaction conditions. Process chemists demand them. Nonuniform heating and difficulties with mixing and temperature measurement are technical constraints that initially limited the scale of microwave chemistry with dry media and have not yet been overcome. Poor reproducibility also has been reported, probably resulting from differences in performance and operation of individual domestic microwave ovens [13-15]. Consequently, most, if not all, of the disclosed applications of dry media are laboratory-scale preparations. However, as discussed in other chapters, this does not prevent their being interesting and useful. 

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