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Two perfectly black parallel plates A and B of equal area facing each other are maintained at constant temperature $T_{A} a n d T_{B} (T_{A} > T_{B}) .$ 99 perfectly black and conducting identical screens of same area as plates are introduced between A and B, parallel to each other having equal space between them. Once the thermal equilibrium is reached. Choose the CORRECT statements: (Take $σ (T_{A}^{4} - T_{B}^{4}) = 5000 \frac{W}{m^{2}}$ ; Ignore convection)

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Effective heat flux between plates A and B reduces due to introduction of screens between them

Heat flux between screen 1 and 2 is greater than heat flux between screen 98 and 99

Heat flux between plate A and screen 1 is $5000 \frac{W}{m^{2}}$

Heat flux between screen 99 and plate B is $50 \frac{W}{m^{2}}$

answer is C, D.

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Detailed Solution

$q_{n e t}^{"}, f = σ (T_{A}^{4} - T_{1}^{4}) = σ (T_{1}^{4} - T_{2}^{4}) ........ = σ (T_{n - 1}^{4} - T_{B}^{4})$

$\Rightarrow σ (T_{A}^{4} - T_{B}^{4}) = (n + 1) q_{n e t}^{"}, f$

$\Rightarrow q_{n e t}^{"}, f = \frac{σ}{(n + 1)} (T_{A}^{4} - T_{B}^{4})$

$\Rightarrow q_{n e t, f}^{"} = \frac{1}{n + 1} \times 5000 = 50 \frac{W}{m^{2}}$

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