A smooth vertical steel tube carries water at a pressure of 10 bars. Saturated liquid water is pumped into the D=0.05 diameter tube at its bottom end (x=0) with a mean velocity of um=0.005 m/s. The tube is exposed to combusting pulverized coal, providing a uniform heat flux of q''=2000 W/m^2 . Determine the tube wall temperature and the quality of the flowing water at x=15 m. Assume Gs, f=1.

Saturated water, liquid (10 bars): Tsat = 452.8 K, \rho = 887.3 kg/m3 , hfg =2014 kJ/kg, \mu L =149.4 × 10- 6 N⋅s/m2 , kL = 0.6766 W/m⋅K, Prl Prl= 0.979;

Water vapor: \rho v = 5.094 kg/m3 , µv = 14.95 × 10-6 N⋅s/m2 , kv = 0.03353 W/m⋅K, Prv = 1.149.