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)

Physics & Space Science

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