Question

For specified inlet and outlet temperatures, for what kind of heat exchanger will the \(\Delta T_{\mathrm{lm}}\) be greatest: double-pipe parallel-flow, double-pipe counterflow, crossflow, or multipass shell-and-tube heat exchanger?

Short answer

Answer: The double-pipe counterflow heat exchanger would result in the greatest logarithmic mean temperature difference for the given inlet and outlet temperatures.

Step-by-step solution

Introduction to Different Types of Heat Exchangers

There are four types of heat exchangers mentioned in this exercise: 1. Double-pipe parallel-flow heat exchanger 2. Double-pipe counterflow heat exchanger 3. Crossflow heat exchanger 4. Multipass shell-and-tube heat exchanger Now, let's compare their operation and temperature profiles to determine which heat exchanger would result in the greatest \(\Delta T_{\mathrm{lm}}\).

Double-Pipe Parallel-Flow Heat Exchanger

In a double-pipe parallel-flow heat exchanger, the hot and cold fluids flow in the same direction. While easy to construct, this design has the disadvantage that the temperature difference between the hot and cold fluids decreases as the fluids move along the exchanger. As a result, the heat transfer rate diminishes, leading to a relatively small \(\Delta T_{\mathrm{lm}}\).

Double-Pipe Counterflow Heat Exchanger

In a double-pipe counterflow heat exchanger, the hot and cold fluids flow in opposite directions. This design allows for a more uniform temperature difference along the length of the heat exchanger, resulting in a more efficient heat transfer and a larger \(\Delta T_{\mathrm{lm}}\) compared to parallel-flow heat exchangers.

Crossflow Heat Exchanger

In a crossflow heat exchanger, the hot and cold fluids flow perpendicular to each other. This design allows for efficient heat transfer between the two fluids even when their flow rates differ significantly. The temperature profiles for crossflow heat exchangers are generally between those of parallel-flow and counterflow heat exchangers, leading to a \(\Delta T_{\mathrm{lm}}\) that is generally greater than parallel-flow but less than counterflow designs.

Multipass Shell-and-Tube Heat Exchanger

A multipass shell-and-tube heat exchanger consists of a shell containing multiple tubes, with the hot and cold fluids flowing through separate tubes. This design allows for multiple passes of the fluids through the heat exchanger, increasing the heat transfer area and resulting in a more efficient heat transfer. The temperature profiles for multipass shell-and-tube heat exchangers depend on the configuration of the passes, but they can achieve greater \(\Delta T_{\mathrm{lm}}\) values than both parallel-flow and crossflow heat exchangers.

Comparison and Conclusion

Based on the analysis of the four different types of heat exchangers, we can rank their ability to achieve high \(\Delta T_{\mathrm{lm}}\) as follows (from highest to lowest): 1. Double-pipe counterflow heat exchanger 2. Multipass shell-and-tube heat exchanger 3. Crossflow heat exchanger 4. Double-pipe parallel-flow heat exchanger Thus, for the specified inlet and outlet temperatures, the double-pipe counterflow heat exchanger will result in the greatest \(\Delta T_{\mathrm{lm}}\).