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Q10. In a counter flow oil cooler, the oil flows with a velocity of 1.2 m/s through a single pass of 35 tubes. Each tube has a bore diameter of 15 mm and wall thickness of 1.6 mm. The oil enters at a temperature of 80°C and leaves at a temperature of 30°C. The fresh water coolant enters at a rate of 7 kg/s and a temperature of 24°C. The overall heat transfer coefficient is 2000 W/m²K, referenced to the tube outer surface area. Calculate EACH of the following:

(a) The total mass flow rate of oil

(b) The outlet temperature of the water

(c) The logarithmic mean temperature difference

(d) The length of each tube.

Note: For water: specific heat capacity 4.2 kJ/kgK

For oil: specific heat capacity 2.0 kJ/kgK, density 860 kg/m³