Detailed knowledge of geometry, fluid parameters, outer radius of cladding, linear heat rate, convective heat transfer coefficient allows us to calculate the temperature difference ∆T between the coolant (Tbulk) and the cladding surface (TZr,1).
To calculate the the cladding surface temperature, we have to know:
- the outer diameter of the cladding is: d = 2 x rZr,1 = 9,3 mm
- the Nusselt number, which is NuDh = 890
- the hydraulic diameter of the fuel channel is: Dh = 13,85 mm
- the thermal conductivity of reactor coolant (300°C) is: kH2O = 0.545 W/m.K
- the bulk temperature of reactor coolant at this axial coordinate is: Tbulk = 296°C
- the linear heat rate of the fuel is: qL = 300 W/cm (FQ ≈ 2.0)
The convective heat transfer coefficient, h, is given directly by the definition of Nusselt number:
Finally, we can calculate the cladding surface temperature (TZr,1) simply using the Newton’s Law of Cooling:
For PWRs at normal operation, there is a compressed liquid water inside the reactor core, loops and steam generators. The pressure is maintained at approximately 16MPa. At this pressure water boils at approximately 350°C(662°F). As can be seen, the surface temperature TZr,1 = 325°C ensures, that even subcooled boiling does not occur. Note that, subcooled boiling requires TZr,1 = Tsat. Since the inlet temperatures of the water are usually about 290°C (554°F), it is obvious this example corresponds to the lower part of the core. At higher elevations of the core the bulk temperature may reach up to 330°C. The temperature difference of 29°C causes the subcooled boiling may occur (330°C + 29°C > 350°C). On the other hand, nucleate boiling at the surface effectively disrupts the stagnant layer and therefore nucleate boiling significantly increases the ability of a surface to transfer thermal energy to bulk fluid. As a result, the convective heat transfer coefficient significantly increases and therefore at higher elevations, the temperature difference (TZr,1 – Tbulk) significantly decreases.