A shell-and-tube heat exchanger consisting of one shell pass and two tube passes is used to transfer heat from an ethylene glycol-water solution (shell side) supplied from a rooftop solar collector to pure water (tube side) used for household purposes. The tubes are of inner and outer diameters D_i = 3.6 mm and D_o = 3.8 mm, respectively. Each of the 100 tubes is 0.8 m long (0.4 m per pass), and the heat transfer coefficient associated with the ethylene glycol-water mixture is h_o = 11.000 W/m² ∙ K.

(a) For pure copper tubes, calculate the heat transfer rate from the ethylene glycol-water solution (m = 2.5 kg/s, T_h,i = 80°C) to the pure water (m = 2.5 kg/s, T_c,i = 20°C). Determine the outlet temperatures of both streams of fluid. The density and specific heat of the ethylene glycol-water mixture are 1040 kg/m³ and 3660 J/kg ∙ K. respectively.

(b) It is proposed to replace the copper tube bundle with a bundle composed of high-temperature nylon tubes of the same diameter and tube wall thickness. The nylon is characterized by a thermal conductivity of k_n = 0.31 W/m ∙ K. Determine the tube length required to transfer the same amount of energy as in part (a).