For a heat exchanger where the temperature difference between hot and cold streams varies along the length ($\Delta T_1 \neq \Delta T_2$), the Logarithmic Mean Temperature Difference (LMTD) compared to the Arithmetic Mean Temperature Difference (AMTD) is always:
Options:
(A) Strictly smaller than the AMTD ($\text{LMTD} < \text{AMTD}$)
(B) Strictly greater than the AMTD ($\text{LMTD} > \text{AMTD}$)
(C) Equal to the AMTD under all flow configurations
(D) Zero whenever fluid boiling occurs
Answer Key:
A
Step-by-Step Solution & Explanation
By the logarithmic mean inequality, $\text{LMTD} = \frac{\Delta T_2 - \Delta T_1}{\ln(\Delta T_2 / \Delta T_1)} < \frac{\Delta T_1 + \Delta T_2}{2} = \text{AMTD}$ for any $\Delta T_1 \neq \Delta T_2$. Using AMTD in design overestimates heat transfer and leads to undersized heat exchangers.