In a counter-flow double pipe heat exchanger, milk is heated from $20^\circ\text{C}$ to $60^\circ\text{C}$ while hot water cools from $90^\circ\text{C}$ to $50^\circ\text{C}$. The Log Mean Temperature Difference (LMTD) in $^\circ\text{C}$ is ________ (answer in integer).
Answer Key:
30
Step-by-Step Solution & Explanation
For counter-flow arrangement:
• Inlet temperature difference $\Delta T_1 = T_{h,in} - T_{c,out} = 90^\circ\text{C} - 60^\circ\text{C} = 30^\circ\text{C}$
• Outlet temperature difference $\Delta T_2 = T_{h,out} - T_{c,in} = 50^\circ\text{C} - 20^\circ\text{C} = 30^\circ\text{C}$
When $\Delta T_1 = \Delta T_2 = \Delta T$, the LMTD is simply:
$\text{LMTD} = \Delta T_1 = \Delta T_2 = 30^\circ\text{C}$