9.105. As for normal nonboiling heat transfer, it is possible to describe the heat-transfer rate for a flow-boiling system in terms of a heat-transfer coefficient and a temperature-difference driving force. However, from the reactor core design viewpoint, the boiling heat-transfer coefficient is not of great significance. With boiling present, heat is transferred from the heated (fuel rod) surface to the liquid coolant by several evaporative mech­anisms resulting in vapor-bubble growth but not requiring much of a tem­perature-difference driving force between the surface and the bulk of the fluid. Since the temperature driving force is small compared with that in nonboiling systems, the designer is primarily concerned with fixing speci­fications to allow a sufficient margin based on the critical heat flux limi­tation. Therefore, the following paragraphs devoted to a discussion of the boiling heat-transfer coefficient are intended for background only.

9.106. It is apparent from Fig. 9.13 that log(q/A) is a linear function of log(ts — tSSLi) over a considerable portion of the nucleate boiling range, so that the general expression

J = C{f, — U", (9.37)

where C and n are constants, is applicable to a particular set of conditions. If the difference between the temperature of the heated surface and the saturation temperature of the coolant is represented by Дtb9 equation (9.37) may be written as

2 = C(Atby.

If hb represents the boiling heat-transfer coefficient, it may be defined by

so that

9.107.

For subcooled or local boiling, the relationship

has been found to be applicable, where q/A is in W/m2, p is the pressure in MPa, and Дtb is in kelvin [13]. In the region of a PWR channel prior to the inception of local boiling, the heat-transfer coefficient is predicted using equation (9.35). Since equation (9.38) applies to the local-boiling region, designers often define the initiation of local boiling as the point where the surface temperatures predicted by the two equations become equal.

9.108. Although the heat-transfer coefficient is of little importance in the design of a BWR, it is often desirable to evaluate the surface temper­ature of the fuel elements corresponding to a desired average heat flux. This temperature may be important from the standpoint of corrosion resist­ance, and it may also serve as a reference for estimating the maximum internal temperature within the fuel element. According to equation (9.38), the temperature difference Atb at the surface is proportional to the 0.25 power of the heat flux. The surface temperature itself would thus appear to be relatively insensitive to changes in the flux.

Example 9.7. Determine the surface temperature of the fuel in a re­actor core under subcooled-boiling conditions at a system pressure of 7.2 MPa when the average heat flux is (a) 0.5 MW/m2 and (b) 5 MW/m2. The saturation temperature of water at this pressure is 288°C.

(a) From equation (9.38),

Щ-г (5 X 10T25 = 6.6 К (6.6°C)

The fuel surface temperature is consequently 288 + 6.6 ~ 295°C. (b) For an average heat flux of 5.0 MW/m2,

Ath = (6.6)(10)025 = 12 К (12°C),

so the fuel surface temperature is 288 + 12 = 300°C. (As stated, the surface temperature is not very sensitive to changes in the heat flux; the temperature increases from 295°C to only 300°C for a tenfold increase in heat flux. However, the higher flux may be above the critical heat flux limit.)