In a convergent-divergent (CD) nozzle of a rocket motor, the wall heat flux is maximum at
Options:
(A) the exit of the divergent portion of the CD nozzle
(B) the entry to the convergent portion of the CD nozzle
(C) the throat of the CD nozzle
(D) the mid-length of the divergent portion of the CD nozzle
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.11)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Matrices & Determinants)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> In a convergent-divergent (CD) nozzle of a rocket motor, the wall heat flux is maximum at
**2. Mathematical Derivation & Physical Analysis**:
1. **Thermodynamic Cycle Equations**:
Net thrust generated by an aircraft engine is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e}$.
2. **Station Parameter Balance**:
Enforcing energy conservation across the compressor and turbine yields the required thermodynamic work and pressure ratio.
3. **Verification**:
Direct evaluation confirms **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"the exit of the divergent portion of the CD nozzle"*: ❌ **INCORRECT**.
- **(B)** *"the entry to the convergent portion of the CD nozzle"*: ❌ **INCORRECT**.
- **(C)** *"the throat of the CD nozzle"*: ✅ **CORRECT**.
- **(D)** *"the mid-length of the divergent portion of the CD nozzle"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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