Water (c_p = 4180 J/kg·K) enters the 2.5-cminternal-diameter tube of a double-pipe counter-flow heat exchanger at 17°C at a rate of 1.8 kg/s. Water is heated by steam condensing at 120°C (h_fg = 2203 kJ/kg) in the shell. If the overall heat transfer coefficient of the heat exchanger is 700 W/m²·K, determine the length of the tube required in order to heat the water to 80°C using

(a) The LMTD method

(b) The ε-NTU method.