A proposed design for a nuclear power plant uses molten lead to remove heat from the reactor core. The heated lead is then used to boil water that drives a steam turbine. Water at 5 atm pressure (Tsat = 152?C) enters a heated section of a pipe at 60?C with a mass flow rate of m? = 2 kg/s.
The pipe is stainless steel (ks = 15 W/m·K) with a wall thickness of 12 mm and an outside diameter of 6.2 cm. The outside surface of the pipe is surrounded by an almost-stationary pool of molten lead at 477?C.
a. At point where the liquid water has a bulk temperature of Tb = 80?C, estimate the inside and outside wall temperatures of the pipe, Twi and Two , to within about 5?C. Neglect entry length and variable properties effects and take β ≈ 0.000118 K-1 for lead.
Hint: Guess an outside wall temperature above 370?C when computing h for the lead.
b. At what distance from the inlet will the inside wall of the pipe reach Tsat? What redesign may be needed?