A vertical, 3.5 m long evaporator tube of 12 mm internal diameter has water flowing through it from bottom to top. The water enters the tube at a pressure of 5.5 MPa, subcooled with a temperature ϑ i...

A vertical, 3.5 m long evaporator tube of 12 mm internal diameter has water flowing through it from bottom to top. The water enters the tube at a pressure of 5.5 MPa, subcooled with a temperature ϑ_i
= 210 ◦C. It is initially heated to the saturation temperature and then partly vaporized. The tube is heated with a constant heat flux q˙ = 7.58 · 105 W/m². Calculate

a) the tube length at which the water reaches the saturation temperature at its centre and

b) the vapour content at the oulet.

The following data are given: saturation temperature ϑ_s(5.5 MPa) = 269.9 ◦C ≈ 270 ◦C, enthalpies: h₁(210 ◦C; 5.5 MPa) = 940 kJ/kg, h(270 ◦C) = 1184.5 kJ/kg, enthalpy of vaporization ∆hv= 1605 kJ/kg; density of the saturated liquid  (270 ◦C) = 768.0 kg/m³, density of the saturated vapour (270 ◦C) = 28.07 kg/m³
. The calculations may be done with constant densities. Mass flux of water ˙m = 10³
kg/m²s.