Question

What does the logarithmic mean temperature difference represent for flow in a tube whose surface temperature is constant? Why do we use the logarithmic mean temperature instead of the arithmetic mean temperature?

Short answer

Answer: The logarithmic mean temperature difference (LMTD) is significant for designing and analyzing heat exchanger performance as it accurately represents the average temperature difference between the hot and cold fluids in a tube with constant surface temperature. The LMTD differs from the arithmetic mean temperature difference (AMTD) because it accounts for the varying temperature differences along the length of the tube, resulting in more precise heat transfer calculations, while AMTD does not accurately capture these changes, leading to inaccuracies.

Step-by-step solution

Understand the logarithmic mean temperature difference (LMTD)

The logarithmic mean temperature difference represents the average temperature difference between the hot and cold fluids along the length of the tube. It's important for designing and analyzing the performance of heat exchangers, where the surface temperature is constant, because it accounts for the change in temperature along the length of the tube properly. It is used to determine the heat transfer rate, which is important for choosing the appropriate size and design of a heat exchanger.

Understand the difference between LMTD and AMTD

The arithmetic mean temperature difference (AMTD) is the simple average of the temperature differences between the hot and cold fluids at the inlet and outlet of the tube. While AMTD is easy to calculate, it doesn't accurately account for the changes in temperature along the length of the tube, leading to inaccuracies in heat transfer calculations.

Explain why LMTD is preferable over AMTD in heat exchangers

The LMTD is preferable over the AMTD when dealing with heat exchangers because it accounts for the varying temperature differences along the length of the tube. The temperature difference between the fluids decreases as the heat is transferred, and the logarithmic mean temperature difference accurately captures this change more effectively than AMTD. This results in a more accurate estimate of the heat transfer rate, allowing for better design and analysis of the heat exchanger system. To sum up, the logarithmic mean temperature difference (LMTD) represents the average temperature difference between the hot and cold fluids in a tube with constant surface temperature, and it is used for designing and analyzing heat exchanger performance. The LMTD is preferable to the arithmetic mean temperature difference (AMTD) because it accurately captures the changing temperature differences along the length of the tube, resulting in more precise heat transfer calculations.