The 1-m-long, tube-within-a-tube heat exchanger, as shown in the sketch, is used to condense steam at 2 atmospheres in the annulus. Water flows in the inner tube, entering at 90°C. The inner tube is made of copper with a 1.27 cm OD and 1.0 cm ID. (a) Estimate the water flow rate required to keep its outlet temperature below 100°C. (b) Estimate the pressure drop and the pumping power for the water in the heat exchanger, neglecting inlet and outlet losses.
GIVEN
? Tube-within-a-tube condenser
? Cooling water flowing in the inner tube
? Steam at 2 atm condensing inside the annulus
FIND
(a) Coolant water flow rate to maintain coolant outlet temperature below 100°C
(b) Coolant pressure drop and pumping power
ASSUMPTIONS
? Steady conditions
? The heat exchanger is horizontal
SKETCH
PROPERTIES AND CONSTANTS
From Appendix 2, Table 13, the properties of water at 2 atm are
(a) We can use Equation (9.23) to calculate the average condensing heat transfer coefficient for a
horizontal tube
where
Assuming that the average coolant temperature is 95°C and neglecting temperature drop across the copper tube, we have Ts = 95°C. Then
The average condensing heat transfer coefficient is then
The average condensing heat transfer coefficient is then
we can solve for the coolant mass flow
(b) To determine the pressure drop and pumping power, we need to determine the Reynolds number for the coolant flow
At the average bulk coolant temperature of 95°C, Table 13 gives
Assuming the tube is smooth, the friction from Figure 7.17 is
F = 0.0165
and Equation (7.13) gives the pressure drop
The mean flow velocity for the coolant is
The pressure drop is then
The pumping power can be determined from Equation (7.19)
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