Reciprocity theorem uses shape factor relations to compute configuration factors between surfaces. For a small sphere under a concentric hemisphere, f12 is (A2/A1) × (1 / (4π × r)), while for the hemisphere above the sphere, f21 is (A1/A2) × (1 / (4π × r)), involving A1, A2, and sphere radius (r) in calculations.
The reciprocity theorem is used to relate the configuration factors between two surfaces, and the basic shape factor relations provide formulas for calculating these factors. In the configuration described, we have a small sphere of area A1 under a concentric hemisphere of area A2. To determine f12, we need to calculate the shape factor for the sphere below the hemisphere, and to determine f21, we need to calculate the shape factor for the hemisphere above the sphere.
For the small sphere below the hemisphere (A1 under A2), the shape factor can be calculated using the formula:
f12 = (A2 / A1) * (1 / (4π * r))
For the hemisphere above the sphere (A2 above A1), the shape factor can be calculated using the formula:
f21 = (A1 / A2) * (1 / (4π * r))
Where A1 and A2 are the surface areas of the sphere and hemisphere respectively, and r is the radius of the sphere. Plug in the values of A1, A2, and r to calculate f12 and f21.