A shell-and-tube counter flow heat exchanger is to be designed for heating an oil from 27°C to 82°C. The heat exchanger has two tube passes and one shell pass. The oil is to pass through 3.8 cm schedule40 pipes at a velocity of 1 m/s and steam is to condense at 102°C on the outside of the pipes. The specific heat of the oil is 1.800 kJ/kg K and its mass density is 925 kg/m³. The steam-side heat transfer coefficient is approximately 10 kW/m² K, and the thermal conductivity of the metal of the tubes is 30 W/m K. The results of previous experiments giving the oil-side heat transfer coefficients for the same pipe size at the same oil velocity as those to be used in the exchanger are:

(a) Find the overall heat transfer coefficient U based on the outer surface area at the point where the oil is 38°C. 

(b) Find the temperature of the inside surface of the pipe when the oil temperature is 38°C.
(c) Find the required length of the tube bundle.

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ΔΤ (°C) Toil (°C) hf (W/m k) 75 27 80 64 53 42 20 38 49 60 71 82 85 100 140 250 540