In a counter-current plate heat exchanger, milk enters at $15^\circ\text{C}$ and exits at $75^\circ\text{C}$. Hot water enters at $90^\circ\text{C}$ and exits at $30^\circ\text{C}$. Calculate the Log Mean Temperature Difference (LMTD) of the heat exchanger in $^\circ\text{C}$.
Answer Key:
15
Step-by-Step Solution & Explanation
Temperature differences at the two ends:
$\Delta T_1 = T_{h,\text{in}} - T_{c,\text{out}} = 90 - 75 = 15^\circ\text{C}$
$\Delta T_2 = T_{h,\text{out}} - T_{c,\text{in}} = 30 - 15 = 15^\circ\text{C}$
When $\Delta T_1 = \Delta T_2$, the LMTD equals this common value:
$\text{LMTD} = 15.0^\circ\text{C}$