A feed water heater that supplies a boiler consists of a shell-and-tube heat exchanger with one shell pass and two tube passes. One hundred thin-walled tubes each have a diameter of 20 mm and a length (per pass) of 2 m. Under normal operating conditions water enters the tubes at 10 kg/s and 290 K and is heated by condensing saturated steam at 1 atm on the outer surface of the tubes. The convection coefficient of the saturated steam is 10.000 W/m² ∙ K.

(a) Determine the water outlet temperature.

(b) With all other conditions remaining the same, but accounting for changes in the overall heat transfer coefficient, plot the water outlet temperature as a function of the water flow rate for 5 < m_c < 20 kg/s.

(c On the plot of part (b), generate two additional curves for the water outlet temperature as a function of flow rate for fouling factors of R'f = 0.0002 and 0.0005 m² ∙ K/W.