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

Answer: Based on the temperature measurements provided, the double-pipe heat exchanger is a counterflow arrangement.

Step-by-step solution

Definitions and Distinctions

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.

Examine the Temperature Measurements

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.

Calculate the Temperature Difference at Inlet and Outlet

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.

Temperature Difference at Inlet

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

Temperature Difference at Outlet

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

Determine the Heat Exchanger Type

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.

Key concepts

Counterflow Heat Exchanger

In a counterflow heat exchanger, the hot and cold fluids move in opposite directions. This arrangement maximizes the temperature gradient between the two fluids, allowing for more efficient heat transfer. The counterflow configuration ensures that the outlet temperature of the cold fluid can be close to the inlet temperature of the hot fluid, which significantly improves efficiency.

Consider the example of a water-to-water heat exchanger where hot water enters at 80°C and exits at 45°C, while cold water enters at 20°C and exits at 50°C. In this scenario, the flow must be counterflow because the cold water exit temperature (50°C) exceeds the hot water exit temperature (45°C).

**Key Benefits of Counterflow Heat Exchangers:**

• Higher efficiency due to maximum temperature gradients.
• Can achieve larger temperature changes in the fluids.
• Cost-effective for processes that require substantial heat transfer.

Understanding the flow pattern is essential to optimizing the heat exchanger design and performance in various industrial applications.

Parallel-flow Heat Exchanger

In a parallel-flow heat exchanger, both the hot and cold fluids flow in the same direction. This type of heat exchanger is usually simpler in design but not as efficient as the counterflow arrangement. In a parallel-flow setting, the temperature difference between the two fluids decreases rapidly along the length of the heat exchanger.

As a result, the lowest possible temperature for the cold fluid is limited by the exit temperature of the hot fluid. Thus, the heat transfer is less efficient, and there is minimal mixing of temperatures between the two streams.

**Important Characteristics of Parallel-flow Heat Exchangers:**

• Simple design and construction.
• Lower thermal efficiency compared to counterflow.
• Useful in applications where simplicity and cost are more important than performance.

Despite its limitations, parallel-flow heat exchangers may still be adequate for processes where temperature overlap is acceptable or where exact temperature control is not critical.

Temperature Difference in Heat Exchangers

The temperature difference between the hot and cold fluids in a heat exchanger is a crucial factor in determining the type of heat exchanger arrangement. It is calculated at two key points: the inlet and outlet. This difference influences the rate of heat transfer, and its behavior assists in identifying whether the exchanger is a parallel-flow or counterflow type.

In the exercise, calculations showed the temperature difference at the inlet as 60°C, while the outlet had a difference of -5°C, confirming a counterflow arrangement.

**Essential Points about Temperature Difference:**

• Greater temperature difference results in more effective heat transfer.
• In counterflow, the temperature difference can change direction as seen in the exercise.
• In parallel-flow, the temperature difference diminishes along the length of the exchanger.

Understanding these differences is vital for designing efficient heat exchangers and ensuring optimal performance in various industrial and engineering processes.