In a Rankine power system, 1.5 kg/s of steam leaves the turbine as saturated vapor at 0.51 bar. The steam is condensed to saturated liquid by passing it over the tubes of a shell-and-tube heat exchanger, while liquid water, having an inlet temperature of Tc,i = 280 K, is passed through the tubes. The condenser contains 100 thin-walled tubes, each of 10-mm diameters and the total water flow rate through the tubes is 15 kg/s. The average convection coefficient associated with condensation on the outer surface of the tubes may be approximated as ho = 5000 W/m2 · K. Appropriate property values for the liquid water are c p = 4178 J/kg · K, µ = 700 x 10-6 kg/s · m, k = 0.628 W/m · K, and Pr = 4.6.
(a) What is the water outlet temperature?
(b) What is the required tube length (per tube)?
(c) After extended use, deposits accumulating on the inner and outer tube surfaces provide a cumulative fouling factor of 0.0003 m2 · K/W. For the prescribed inlet conditions and the computed tube length, what mass fraction of the vapor is condensed?
(d) For the tube length computed in part (b) and the fouling factor prescribed in part (c), explore the extent to which the water flow rate and inlet temperature may be varied (within physically plausible ranges) to improve the condenser performance. Represent your results graphically, and draw appropriate conclusions.
