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Q7. An air- cooled heat exchanger has 9 tubes each of 40 mm mean diameter in a single pass, parallel flow arrangement.

Fresh water flows through the tubes with a velocity of 0.2 m/s. It enters at a temperature of 85℃ and leaves at a temperature of 75℃. The air enters the cooler at a temperature of 4℃ and has a mass flow of 9 kg/s.

(a) Calculate EACH of the following.

(i) The rate of heat transfer from the water; (3)

(ii) The log means temperature difference for the cooler; (5)

(iii) The length of EACH cooler tube. (5)

(b) Sketch the cooler temperature distribution (profile) diagram (3)

Note: for air c_p =1.005  kJ⁄(kg K)

for water c = 4.2  kJ⁄(kg K)

heat transfer coefficient for air side of the tube = 8.84  kW⁄(m² K)

heat transfer coefficient for water side of the tube = 13.74  kW⁄(m² K).