Question Bank • QB_EXP_DFE_HEX_004 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Heat Exchangers: LMTD & NTU-Effectiveness Methods

Subtopic: Counterflow heat exchanger LMTD calculation

Question Statement:

In the counterflow heat exchanger temperature profile diagram, hot juice is cooled from $80^\circ\text{C}$ to $40^\circ\text{C}$ by water heated from $15^\circ\text{C}$ to $35^\circ\text{C}$. Determine the Logarithmic Mean Temperature Difference ($LMTD$) in $^\circ\text{C}$ (round off to one decimal place).

Answer Key:

34.1

Step-by-Step Solution & Explanation

$\Delta T_1 = 80 - 35 = 45^\circ\text{C}$. $\Delta T_2 = 40 - 15 = 25^\circ\text{C}$. $LMTD = \frac{45 - 25}{\ln(45/25)} = \frac{20}{\ln(1.8)} = \frac{20}{0.5878} \approx 34.03^\circ\text{C}$.
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