A shell-and-tube heat exchanger is used for cooling 47 kg/s of a process stream flowing through the tubes from 160 C to 100°C. This heat exchanger has a total of 100 identical tubes, each with an inside diameter of 2.5 cm and negligible wall thickness. The average properties of the process stream are: rho 950 kg/m3, k = 0.50 w/m. K, cp-3.5 kJ/kg-K and μα 2.0 mPa-s. The coolant stream is water (cp- 4.18 kJ/kg K) at a flow rate of 66 kg/s and an inlet temperature of 10 C, which yields an average shell-side heat transfer coefficient of 4.0 kW/m2-K. Calculate the tube length if the heat exchanger has

(a) a 1-shell pass and a 1-tube pass and
(b) a 1-shell pass and 4-tube passes 1.