Question 10

NUMERICALMEDIUM

Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures TPT_P and TQT_Q, respectively, with TQ<TPT_Q < T_P, as shown in Fig. 1. The radiated power transferred per unit area from P to Q is W0W_0. Subsequently, two more plates, identical to P and Q, are introduced between P and Q, as shown in Fig. 2. Assume that heat transfer takes place only between adjacent plates. If the power transferred per unit area in the direction from P to Q (Fig. 2) in the steady state is WSW_S, then the ratio W0WS\frac{W_0}{W_S} is ___

Question
Correct Answer: 3

Detailed Solution

The net rate of radiation heat transfer between two large parallel black plates is given by W0=σ(TP4−TQ4)W_0 = \sigma(T_P^4 - T_Q^4). When nn identical blackbody radiation shields (plates) are inserted between them, the new steady-state power transfer WSW_S is given by the formula: WS=1n+1W0W_S = \frac{1}{n+1} W_0 In this problem, two more identical plates are introduced between P and Q, so n=2n = 2. Therefore: WS=W02+1=W03W_S = \frac{W_0}{2+1} = \frac{W_0}{3} Rearranging for the ratio: W0WS=3\frac{W_0}{W_S} = 3

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