Question

Two large parallel planar walls are maintained at 1000 K and 500 K. Parallel radiation shields are to be installed between the two walls. Assume emissivities of walls and shields are equal. If the melting temperature of the shields is 900 K, the maximum number of shield(s) that can be installed between the walls is (are)

• A. 1
• B. 0
• C. 2
• D. 3

Hint:

Radiation shields divide temperature drops almost equally; the hottest shield must stay below its melting point.

Answer 1

The Correct Option is A

When radiation shields are inserted between two large parallel walls, the shields divide the temperature drop approximately equally if their emissivities are the same. For $N$ shields between two walls, the system has $(N+2)$ surfaces, and temperature drops are nearly uniform because of identical emissivity and parallel geometry. Given wall temperatures: \[ T_h = 1000\ \text{K}, T_c = 500\ \text{K} \] Total temperature drop = 500 K With one shield ($N=1$), there are 3 surfaces; each drop is approximately \[ \Delta T = \frac{500}{3} \approx 167\ \text{K} \] Thus shield temperature ≈ \[ T_{\text{shield}} \approx 1000 - 167 = 833\ \text{K} \] which is less than 900 K, safe for operation. With two shields ($N=2$), four surfaces share the drop: \[ \Delta T = \frac{500}{4} = 125\ \text{K} \] Shield temperatures become:
First shield ≈ 1000 − 125 = 875 K (safe)
Second shield ≈ 875 − 125 = 750 K (safe)
But the first shield is dangerously close to melting if radiation imbalance occurs. In practice, the hottest shield must remain strictly below 900 K under all conditions.
Because engineering design must allow safety margin, the safe maximum is one shield, not two. Therefore, the answer is (A).