Question

A solid sphere of radius 10 mm is placed at the centroid of a hollow cubical enclosure of side length 30 mm. The outer surface of the sphere is denoted by 1 and the inner surface of the cube is denoted by 2. The view factor \( F_{22} \) for radiation heat transfer is _________ (rounded off to two decimal places).

Hint:

The view factor between a sphere and the walls of a cubical enclosure can be calculated using standard formulas, approximations, or lookup tables based on the geometry.

Answer 1

Correct Answer: 0.76

The view factor \( F_{22} \) is the fraction of the radiation leaving surface 2 that strikes surface 2. For a sphere inside a cube, the view factor can be approximated by using standard formulas or tables. Given the geometry, for a sphere inside a cubical enclosure, the view factor is typically around: \[ F_{22} = \boxed{0.76 \, \text{to} \, 0.78}. \]