Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
A counter-current double-pipe heat exchanger is used to cool milk from 70°C to 20°C using chilled water entering at 5°C and leaving at 15°C. The Log Mean Temperature Difference (LMTD) of the heat exchanger in °C is ________ (rounded off to 2 decimal places).
Answer Key:
31.24
Step-by-Step Solution & Explanation
1. For counter-current flow:
- Terminal 1: Milk in at 70°C, Water out at 15°C $\implies \Delta T_1 = 70 - 15 = 55^\circ\text{C}$.
- Terminal 2: Milk out at 20°C, Water in at 5°C $\implies \Delta T_2 = 20 - 5 = 15^\circ\text{C}$.
2. Logarithmic Mean Temperature Difference:
$\text{LMTD} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)} = \frac{55 - 15}{\ln(55 / 15)} = \frac{40}{\ln(3.6667)} = \frac{40}{1.29928} = 30.785^\circ\text{C} \approx 30.79^\circ\text{C}$
(Acceptable range 30.7 to 31.3°C).