Question

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.

Short answer

Explain your conclusion. Answer: The given heat exchanger is most likely a parallel-flow arrangement. This conclusion is based on the observation that the temperature difference between the hot and cold fluids decreases from the entrance point to the exit point. This characteristic aligns with parallel-flow heat exchangers, whereas in counterflow heat exchangers, the temperature difference remains relatively constant throughout.

Step-by-step solution

Examine parallel-flow and counterflow heat exchangers

In a parallel-flow heat exchanger, the fluids flow in the same direction. The temperature difference between the two fluids is the highest at the entrance point and lowest at the exit point. In a counterflow heat exchanger, the two fluids flow in opposite directions. As a result, the temperature difference between the two fluids remains relatively constant along the length of the exchanger, which leads to a more efficient heat transfer.

Compare temperature differences in the given data

First, let's calculate the difference in temperature between the two fluids at the entrance and the exit points. Entrance temperature difference: \(|T_{Hin} - T_{Cin}| = |80^{\circ} \mathrm{C} - 20^{\circ} \mathrm{C}| = 60^{\circ} \mathrm{C}\) Exit temperature difference: \(|T_{Hout} - T_{Cout}| = |45^{\circ} \mathrm{C} - 50^{\circ} \mathrm{C}| = 5^{\circ} \mathrm{C}\)

Analyze the temperature differences and determine the flow arrangement

Based on the calculated temperature differences, we can observe the following: - In the given data, the temperature difference at the entrance is higher than at the exit, which indicates a decrease in temperature difference over the length of the heat exchanger. - In a parallel-flow heat exchanger, we expect a decrease in temperature difference from the entrance to the exit as the fluids flow in the same direction. - In a counterflow heat exchanger, the temperature difference between fluids remains relatively constant along the length of the exchanger, which is not consistent with the given data. Considering these findings, it is more likely that the given heat exchanger is a parallel-flow heat exchanger.