A hemispherical furnace of 1 m radius has the inner surface

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A hemispherical furnace of 1 m radius has the inner surface (emissivity, ε = 1) of its roof maintained at 800 K, while its floor (ε = 0.5) is kept at 600 K. Stefan-Boltzmann constant is 5.668 × 110^-8W/m²K⁴. The net radiative heat transfer (in kW) from the roof to the floor is _______.

1. 22 kW.
2. 25 kW.
3. 24.9 kW.
4. 24. kW.

Correct Option: C

Let the base be (1) and hemispherical furnace be (2)
∴ F₁₁ + F₁₂ = 1 ...(1)
F₂₁ + F₂₂ = 1 ...(2)
∵ F₁₁ = 0
∴ F₁₂ = 2
A₁ F₁₂ = A₂ F₂₁

∴ F₂₁ =	A₁	F₁₂ =	πR²	F₁₂ = 0.5F₁₂
	A₂		2πR²

∴ F₂₁ = 0.5 × 2.0.5
∴ F₂₂ = 0.5
So, F₁₁ = 0, F₁₂ = 1, F₂₁ = 0.5 < F₂₂ = 0.5
Now Radiative heat transfer,
⇒ Q = A₁ F₁₂ε₂ × 6(800⁴ – 600⁴) watt
∴ Q = π × 1² × 1 × 0.5 × 5.668 × 10^{– 8}(800⁴ – 600⁴) watt
or Q = 24.9 kW.