A shell-and-tube heat exchanger is used for the heating of oil from 20°C to 30°C ; the oil flow rate is 12 kg/s (C_po = 2.2 kJ/kg · K). The heat exchanger has one shell pass and two tube passes. Hot water (C_pw = 4.18 kJ/kg · K) enters the shell at 75°C and leaves the shell at 55°C. The overall heat-transfer coefficient based on the outside surface of the tubes is estimated to be 1080 W/m² · K. Determine 

a. The corrected logarithmic-mean temperature difference 

b. The required surface area in the exchanger