A counterflow heat exchanger through which passes 12.5 kg/s of air to be cooled from 540ºC to 140ºC, contains 4200 tubes, each having a diameter of 30 mm. The inlet and outlet temperatures of cooling...

A counterflow heat exchanger through which passes 12.5 kg/s of air to be cooled from 540ºC to 140ºC, contains 4200 tubes, each having a diameter of 30 mm. The inlet and outlet temperatures of cooling water are 25C and 75C respectively. If the water side resistance to flow is regligible, calculate the tube length required for this duty. For turbulent flow inside tubes, you can use:
Pr^0.4
 Properties of the air at the average temperature are as follows:

 = 1.009 kg/m³, c_p
= 1.0082 kJ/kgC,
 = 2.075
 10^–5
kg/ms and k = 3.003
 10^–2
W/ m²K.