Cold water (cp = 4180 J/kg · K) enters the tubes of a heat exchanger with 2-shell passes and 23-tube passes at 14°C at a rate of 3 kg/s, while hot oil (c_p = 2200 J/kg · K) enters the shell at 200°C at the same mass flow rate. The overall heat transfer coefficient based on the outer surface of the tube is 300 W/m² · K and the heat transfer surface area on that side is 20 m². Determine the rate of heat transfer using

(a) The LMTD method

(b) The ε-NTU method.