Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Which one of the following is the unit of heat transfer coefficient?
Options:
(A) W m' K-1
(B) W mªK
(C) Wm? K-1
(D) Wm?K
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2019 Q.26)**
**1. Governing Concept**:
- **Topic**: Heat Transfer & SI Units of Transport Phenomena
- In convective and conductive heat transfer across an interface, Newton's law of cooling is:
$\dot{Q} = h A \Delta T$
where $\dot{Q}$ is heat transfer rate in Watts ($\text{W} = \text{J/s}$), $A$ is surface area in $\text{m}^2$, $\Delta T$ is temperature difference in Kelvin ($\text{K}$) or $^\circ\text{C}$, and $h$ is the heat transfer coefficient.
- Solving for the dimensions of $h$:
$h = \frac{\dot{Q}}{A \Delta T} \implies \text{SI Units} = \frac{\text{W}}{\text{m}^2 \cdot \text{K}} = \text{W} \cdot \text{m}^{-2} \cdot \text{K}^{-1}$
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Dimension of thermal conductivity $k$ ($\text{W} \cdot \text{m}^{-1} \cdot \text{K}^{-1}$).
- **Option (B) is INCORRECT**: Lacks temperature dimension.
- **Option (C) [W m⁻² K⁻¹] is CORRECT**: Precise SI unit of convective heat transfer coefficient.
- **Option (D) is INCORRECT**: Heat flux unit ($\text{W/m}^2$), missing temperature.
**3. Final Answer**:
- **Correct Choice**: **C**
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