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Q7. An annular water jacket surrounds a 200 mm mean diameter pipe carrying a hot gas, in a counter flow arrangement.

The hot gas enters the cooler with a velocity of 3 m/s and a temperature of 527℃, it leaves a temperature of 50℃.

The cooling water enters the cooler at 15℃ and has a flow rate of 900 kg/hour.

The wall thickness of the pipe may be ignored.

(a) Calculate EACH of the following:

(i) The rate of heat of transfer across the cooler; (2)

(ii) The exit temperature of the water;(2)

(iii) The log mean temperature difference; (4)

(iv) The length of the cooler. (5)

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

Notre: for cooling water C = 4.19 kJ/kg K

For the hot gas C_p = 1.169 kJ/kg K, specific volume = 1.493 m³/kg

The inner surface heat transfer coefficient = 0.2 kW/m² K

The outer surface heat transfer coefficient = 1.25 kW/m² K