Extension to three dimensional emitters – Configuration factor between a sphere and a differential element placed at a random position

After analyzing the previous form factors for the circle, a new question can be deducted. A sphere can be considered, in terms of radiative transfer as a circle [7], as the viewed area of the said sphere from a distant point equals always a circle, because only half of the emitter is visible. Let us consider as emitting source a sphere of radius r, and a differential element, placed randomly in space at a distance (x, y,z), referenced to the three coordinate directions as shown in figure 5:



Figure 5. Calculations parameters for the sphere and a differential element at a random position


The differential element, as in former cases, is defined by its normal, and it is necessary to find the radiation vector Fr impinging on it. Obtaining the modulus (configuration factor) is a direct operation, the angles formed by the unit element are already known:

hr I = Fd 1-x ‘c°sa + Fd,-, cos b + Fdi-z cos7 (54)

And expanding each of them,






d і у /7 2 2 2 3


x + у + z )3







Updated: August 18, 2015 — 12:57 pm