Hot water (c_ph = 4188 J/kg·K) with mass flow rate of 2.5 kg/s at 100°C enters a thin-walled concentric tube counter-flow heat exchanger with a surface area of 23 m² and an overall heat transfer coefficient of 1000 W/m²·K. Cold water (c_pc = 4178 J/kg·K) with mass flow rate of 5 kg/s enters the heat exchanger at 20°C, determine

(a) The heat transfer rate for the heat exchanger

(b) The outlet temperatures of the cold and hot fluids. After a period of operation, the overall heat transfer coefficient is reduced to 500 W/m²·K, determine

(c) The fouling factor that caused the reduction in the overall heat transfer coefficient.