Problem #3: A double-pipe counter-flow heat exchanger is to cool ethylene glycol (Cp = 2560 J/kg- °C) flowing at a rate of 3.5 kg/s from 80°C to 40°C by water (Cp=4180 J/kg-°C) that enters at 20°C and leaves at 55°C. The overall heat transfer coefficient based on the inner surface area of the tube is 250 W/m² °C. Determine (a) the rate of heat transfer, (b) the mass flow rate of water, and (c) the heat transfer surface area on the inner side of the tube. Problem # 4: A shell-and-tube heat exchanger with 2-shell passes and 12-tube passes is used to heat water (Cp = 4180 J/kg °C) in the tubes from 20°C to 70°C at a rate of 4.5 kg/s. Heat is supplied by hot oil (Cp = 2300 J/kg-°C) that enters the shell side at 170°C at a rate of 10 kg/s. For a tube-side overall heat transfer coefficient of 600 W/m² °C, determine the heat transfer surface area on the tube side. Problem # 5: Hot oil (Cp = 2200 J/kg °C) is to be cooled by water (Cp 4180 J/kg °C) in a 2-shell-pass and 12-tube-pass heat exchanger. The tubes are thin-walled and are made of copper with a diameter of 1.8 cm. The length of each tube pass in the heat exchanger is 3 m, and the overall heat transfer coefficient is 340 W/m² °C. Water flows through the tubes at a total rate of 0.1 kg/s, and the oil through the shell at a rate of 0.2 kg/s. The water and the oil enter at temperatures 18°C and 160°C, respectively. Determine the rate of heat transfer in the heat exchanger and the outlet temperatures of the water and the oil. Problem #6: Cold water (Cp = 4180 J/kg-°C) leading to a shower enters a thin-walled double-pipe counter-flow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (Cp=4190 J/kg-°C) that enters at 100°C at a rate of 3 kg/s. If the overall heat transfer coefficient is 950 W/m² °C, determine the rate of heat transfer and the heat transfer surface area of the heat exchanger using the ε- NTU method.