Question

Consider two double-pipe counter-flow heat exchangers that are identical except that one is twice as long as the other one. Which heat exchanger is more likely to have a higher effectiveness?

Short answer

And why? Answer: The heat exchanger that is twice as long as the other one is expected to have a higher effectiveness. This is because the longer heat exchanger provides a greater contact area between the two fluids, allowing for more heat transfer to occur, which results in higher effectiveness.

Step-by-step solution

Define effectiveness of a heat exchanger

In the context of heat exchangers, effectiveness is defined as the ratio between the actual amount of heat transfer and the maximum heat transfer possible. In other words, effectiveness quantifies how well the heat exchanger is performing, compared to an ideal situation. Higher effectiveness means better performance.

Understand the impact of heat exchanger length on effectiveness

In a double-pipe counter-flow heat exchanger, heat is transferred between two fluids flowing in opposite directions. The longer the heat exchanger, the more contact area between the flowing fluids, which leads to greater heat transfer. Thus, an increase in the length of a heat exchanger is expected to increase its effectiveness.

Compare the effectiveness of the two heat exchangers

We have two heat exchangers that are identical except for their lengths. One is twice as long as the other. Recall that the effectiveness of a heat exchanger increases with its length. So, the heat exchanger that is twice as long should have a higher effectiveness than the shorter one.

Conclusion

The heat exchanger that is twice as long as the other one is more likely to have a higher effectiveness. This is because the longer heat exchanger provides a greater contact area between the two fluids allowing for more heat transfer to occur, which results in higher effectiveness.

Key concepts

Double-Pipe Counter-Flow Heat Exchanger

A double-pipe counter-flow heat exchanger is an efficient heat exchange system where two fluids flow in opposite directions. This configuration enables maximum heat transfer because the temperature difference between the hot and cold fluids can be maintained along the entire length of the exchanger.

In a counter-flow setup, as one fluid enters the exchanger hot, it flows parallel but in the opposite direction to the cooler entering fluid. This setup ensures that, at every point along the exchanger, the temperature gradient is maintained, allowing effective heat transfer. Compared to other configurations such as parallel flow, counter-flow provides a higher potential for heat transfer because it utilizes the entire length of the exchanger for maintaining a temperature difference. This makes it a popular choice in processes where high efficiency is required.

• Efficient use of temperature differences
• Greater potential for heat transfer
• Consistently maintains temperature gradient

Heat Transfer Principles

Heat transfer in a heat exchanger follows the basic principles of thermodynamics, which involve conduction and convection. Conduction occurs when heat moves through a material, and convection occurs when heat is transferred through a fluid medium.

In a double-pipe heat exchanger, both principles are at work. The heat from the hotter fluid is conducted through the walls of the inner pipe. At the same time, convection occurs within each fluid as the heat energy is transferred from the hotter fluid to the cooler one. The rate of heat transfer depends on the temperature difference, the thermal properties of the materials, and the surface area available for heat exchange.

• Conduction through the pipe wall
• Convection within the fluids
• Influenced by temperature difference and surface area

Understanding these principles helps in designing and optimizing heat exchangers for various industrial applications where controlling heat energy is crucial.

Impact of Heat Exchanger Length

The length of a heat exchanger plays a significant role in its effectiveness because it directly influences the contact area available for heat transfer. The relationship is simple: a longer heat exchanger provides more contact area, increasing the potential for heat transfer between the two fluids.

When a heat exchanger is longer, the two fluids in the counter-flow exchanger have prolonged contact, which enhances the heat transfer process. This increased contact time and area allow for a greater exchange of thermal energy, resulting in higher effectiveness. However, the benefits of increasing length must be balanced with factors such as pressure drop and cost.

• Longer length equals more contact area
• More contact enhances thermal energy exchange
• Needs to be balanced with pressure drop and cost

In essence, for heat exchangers that are designed with longer lengths, improvements in effectiveness can be significant, which makes them ideal for high-efficiency requirements.