The GATE Grind

GATE 2022 CH – Question 41

Heat Transfer · Radiation · 2 marks · Multiple choice

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 that the emissivities of the walls and the 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)

  1. 1
  2. 0
  3. 2
  4. 3

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Show answer and explanation

Correct answer: (A) 1

Explanation

With $n$ shields of equal emissivity the net flux is divided into $n + 1$ equal steps of $T^4$. The hottest shield, next to the 1000 K wall, has $T_s^4 = T_1^4 - \frac{T_1^4 - T_2^4}{n + 1}$. Here $T_1^4 - T_2^4 = 9.375 \times 10^{11}$. For $n = 1$: $T_s^4 = 10^{12} - 4.69 \times 10^{11} = 5.31 \times 10^{11}$, so $T_s = 854$ K (below 900 K). For $n = 2$: $T_s^4 = 10^{12} - 3.125 \times 10^{11} = 6.875 \times 10^{11}$, so $T_s = 911$ K, which is above the melting temperature. So at most 1 shield.