Question:
Cooling water enters the cooling coil of a fermenter at $7$°C and leaves at $27$°C because it picks up the heat generated due to microbial growth. The culture temperature is $37$°C. The average temperature difference which is used to calculate the rate of heat transfer is:
Cooling water enters the cooling coil of a fermenter at $7$°C and leaves at $27$°C because it picks up the heat generated due to microbial growth. The culture temperature is $37$°C. The average temperature difference which is used to calculate the rate of heat transfer is:
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Heat Exchanger = LMTD (Logarithmic Mean Temperature Difference).
Updated On: May 14, 2026
- Arithmetic mean of 10 and 30
- Geometric mean of 10 and 30
- Logarithmic mean of 10 and 30
- Harmonic mean of 10 and 30
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The Correct Option is C
Solution and Explanation
Step 1: Concept
In heat exchangers (like cooling coils), the temperature difference between the two fluids varies along the length of the exchanger.
Step 2: Analysis
Let $\Delta T_1 = 37 - 7 = 30$°C and $\Delta T_2 = 37 - 27 = 10$°C.
Step 3: Meaning
To accurately calculate the heat transfer rate ($Q = UA\Delta T_m$), the Logarithmic Mean Temperature Difference (LMTD) is used because it accounts for the non-linear temperature change.
Step 4: Conclusion
The LMTD is the standard "average" used for such engineering calculations. Final Answer: (C)
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