Question

A solid cylinder (surface 2) is located at the centre of a hollow sphere (surface 1). The diameter of the sphere is 1 m, while the cylinder has a diameter and length of 0.5 m each. The radiation configuration  factor F₁₁ is 
1. 0.375
2. 0.625
3. 0.75
4. 1

Answer 1

Correct Answer - Option 2 : 0.625

Concept:

For the surface-1:

F11 + F12 = 1

For the surface-2:

\(F_{21} + F_{22} =1\)

From the theorem of reciprocity,

\(A_2F_{21} = A_1F_{12}\)

Calculation:

Given:

d₁ (diameter of sphere) = 1 m, d₂ (diameter of cylinder) = 0.5 m, h = d (Height of cylinder) = 0.5 m.

\(A_1 =4\pi r_1^2=4π \frac {d_1 ^2}4= π d_1 ^2\Rightarrow π ~m^2\)

\(A_2 =\pi d_2h_2\;+\;2\frac{\pi}{4}d_2^2= \frac{3}{2}\pi d_2^2\Rightarrow 0.375\pi\;m^2\)

And we know that,

\(F_{21}=1\) (as the surface-1 is convex, all the radiation radiated by surface 1 will be absorbed by surface 2).

From the theorem of reciprocity,

A₁F₁₂ = A₂F₂₁

∴ π × F₁₂ = 0.375π × F₂₁

∴ F₁₂ = 0.375

Now,

F₁₁ + F₁₂ = 1

F₁₁ + 0.375 = 1

∴ F₁₁ = 0.625.