A solid sphere of radius 10 mm is placed at the centroid of a hollow c...
Given data:
- Radius of the solid sphere (r) = 10 mm
- Side length of the hollow cubical enclosure (L) = 30 mm
- Outer surface of the sphere denoted by 1
- Inner surface of the cube denoted by 2
Calculation:
To calculate the view factor F22 for radiation heat transfer, we need to consider the geometry of the system.
Step 1: Calculation of the surface areas
The surface area of the sphere (A1) can be calculated using the formula:
A1 = 4πr2
Substituting the radius (r = 10 mm) into the formula, we get:
A1 = 4π(102)
A1 = 400π mm2
The surface area of the cube (A2) can be calculated using the formula:
A2 = 6L2
Substituting the side length (L = 30 mm) into the formula, we get:
A2 = 6(302)
A2 = 5400 mm2
Step 2: Calculation of the view factor
The view factor F22 is defined as the fraction of radiation leaving surface 2 that strikes surface 2. In this case, surface 2 is the inner surface of the cube.
The view factor can be calculated using the formula:
F22 = A2/A1
Substituting the values of A2 and A1 into the formula, we get:
F22 = 5400/400π
F22 ≈ 0.7641 (rounded to two decimal places)
Final answer:
The view factor F22 for radiation heat transfer is approximately 0.7641.