Consider a water-to-water double-pipe heat exchanger whose flow arrangement is not known. The temperature measurements indicate that the cold water enters at \(20^{\circ} \mathrm{C}\) and leaves at \(50^{\circ} \mathrm{C}\), while the hot water enters at \(80^{\circ} \mathrm{C}\) and leaves at \(45^{\circ} \mathrm{C}\). Do you think this is a parallel-flow or counterflow heat exchanger? Explain.

In a double-pipe heat exchanger, hot and cold fluids flow inside and between two separate pipes, exchanging heat as they move. In a parallel-flow arrangement, both fluids flow in the same direction. On the other hand, in a counterflow arrangement, the fluids flow in opposite directions. The behavior of temperature difference between the hot and cold streams enables us to determine the type of the heat exchanger.

We have the following temperature measurements: - Cold water: enters at 20°C and leaves at 50°C - Hot water: enters at 80°C and leaves at 45°C Let's first determine the temperature difference between the hot and cold water streams at the inlet and outlet points.

At the inlet, the temperature difference (∆T_in) is the difference between the hot water's entering temperature and the cold water's entering temperature: ∆T_in = T_hot_in - T_cold_in At the outlet, the temperature difference (∆T_out) is the difference between the hot water's leaving temperature and the cold water's leaving temperature: ∆T_out = T_hot_out - T_cold_out Using the given temperatures, we calculate ∆T_in and ∆T_out.

The temperature difference at the inlet is: ∆T_in = 80°C - 20°C = 60°C

The temperature difference at the outlet is: ∆T_out = 45°C - 50°C = -5°C

Based on the calculated temperature differences, we observe: 1. At the inlet, the hot water stream is warmer than the cold water by 60°C. 2. At the outlet, the cold water stream is warmer than the hot water by 5°C. This pattern of temperature difference indicates that the hot and cold water streams are flowing in opposite directions, making it a counterflow heat exchanger. In a parallel-flow arrangement, you would expect the hot stream to be warmer than the cold stream for the entire length of the exchanger, which is not the case here. Since the hot water is leaving at a lower temperature than the cold water, it is evident that the hot and cold water streams are moving counter to each other. In conclusion, based on the temperature measurements provided, it can be determined that this double-pipe heat exchanger is a counterflow arrangement.