Steam exiting the turbine of a power plant passes through the insulated shell-andtube heat exchanger condenser. The mass flow rate of the steam is 145 kg/s, and the steam enters the heat exchanger as a saturated mixture with a quality of 0.95 at 20 kPa. The steam exits the condenser as a saturated liquid at 20 kPa. Liquid cooling water is used to condense the steam. The cooling water enters the condenser at 10oC.

Question

(a) Determine the exit temperature of the liquid cooling water if the mass flow rate is 4000 kg/s.
(b) Using your heat exchanger model, plot the cooling water mass flow rate and volumetric flow rate (entering the condenser) for exit temperatures ranging from 15oC to 55oC.
(c) If the exit temperature of the cooling water is regulated such that it must be no greater than 40oC, and if the cooling water flow rate through the condenser can be adjusted in a range from 500 kg/s to 2000 kg/s, what is the range of maximum possible flow rates of steam through the condenser?

Given: P1 = 20 kPa; x1 = 0.95; m?s = 145 kg/s; P2 = 20 kPa; x2 = 0
T3 = 10oC, m?cw = 4000 kg/s
Assume: Q? = 0 (insulated). Also, given no other information regarding the heat exchanger, make the following common heat exchanger assumptions: W? = ?KE = ?PE = 0
Also, assume the heat exchanger is a multiple-inlet, multiple-outlet, steady-state, steady-flow device.

What will be an ideal response?

Answer 1

(a) Consider the cooling water to be an incompressible substance with constant specific heats: ccw = 4.18 kJ/kg-K: Then ?hcw = ccw ?Tcw

The First Law reduces to m?s(h1 ? h2) = m?cw(h4 ? h3)

Substituting and solving for the cooling water exit temperature:

T4 = m?s(h1 ? h2) /m?cwcp,cw +T3

For the steam: h1 = 2491.79 kJ/kg; h2 = 251.40 kJ/kg

Solving: T4 = 29.4°C

(b) For the volumetric flow rate, use a water density of 1000 kg/m3: V?3 = m?cw/?cw

For the range of exit temperatures of the cooling water:





Note: For small temperature changes of the cooling water, large flow rates are needed. Also note, a large mass of liquid water does not occupy an extremely large volume.



(c) Take T4 = 40°C. The mass flow rate of the steam is then found from the First Law:

m?s = m?cwccw(T4 ? T3)/(h1 ? h2)



For the range of cooling water mass flow rates:



The range of maximum possible flow rates for the steam is 28 kg/s to 112 kg/s.