Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
For a double-pipe heat exchanger, the inside and outside heat transfer coefficients
are 100 and 200 W m-2 K-1, respectively. The thickness and thermal conductivity
of the thin-walled inner pipe are 1 cm and 10 W m-1 K-1, respectively. The value
of the overall heat transfer coefficient is ___________ W m-2 K-1.
Options:
(A) Q.016
(B) 42.5
(C) 62.5
(D) 310
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2022 Q.13)**
**1. Governing Concept**:
- **Topic**: Heat Transfer & Overall Heat Transfer Coefficient
- In a double-pipe heat exchanger, the overall heat transfer coefficient based on outside area ($U_o$) or inside area ($U_i$) is given by:
$\frac{1}{U_o A_o} = \frac{1}{h_i A_i} + \frac{\ln(r_o/r_i)}{2\pi k L} + \frac{1}{h_o A_o}$
- Neglecting tube wall resistance and fouling:
$\frac{1}{U} \approx \frac{1}{h_i} + \frac{1}{h_o}$
- If one heat transfer coefficient is significantly smaller than the other (e.g., $h_i \ll h_o$), the smaller coefficient dominates the thermal resistance, and $U \approx h_{\text{smaller}}$.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: $U$ is always smaller than both individual film coefficients.
- **Option (B) is INCORRECT**: Arithmetic mean is invalid for reciprocal resistances in series.
- **Option (C) is CORRECT**: Formally validated by heat exchanger thermal resistance equations.
- **Option (D) is INCORRECT**: Erroneous resistance relation.
**3. Final Answer**:
- **Correct Choice**: **C**
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