A body 1 in the form of a sphere of 2 cm radius at temperature T₁ is located in body 2, which is a hollow cube of 5 cm side and is at temperature T₂ (T₂ < T₁). The shape factor F₂₁ for radiation heat transfer becomes:

Concept:

Shape Factor is defined as the fraction of radiation energy leaving a surface that reaches another surface, for example, F12 means the fraction of energy leaving the surface 1 reaches surface 2.

.Summation Rule: F₁₁ + F₁₂ = 1

Reciprocity theorem: A₁ F₁₂ = A₂ F₂₁ (A is the surface area)

Calculation:

Let 1 denote the sphere and 2 denote the cube

Given, radius of the sphere = 2 cm, side of the cube = 5 cm

For sphere F₁₁ = 0, F₁₂ = 1 (All radiations from sphere fall on the cube)

A₁ = 4πr²

A₂ = 6a²

Reciprocity theorem

A₁ F₁₂ = A₂ F₂₁   

\({F_{21}} = \frac{{{A_1}}}{{{A_2}}} = \;\frac{{4\pi {2^2}}}{{6\; \times \;{5^2}}} = 0.335\;\;\)