New configuration factor between a circle, a sphere and a differential area at random positions

•Mathematical treatment of circular and semicircular emitters.•Mathematical treatment of spherical emitters.•Mathematical support for computer simulation software.•New configuration factor for semicircular emitters.

In this Note, a configuration factor between a circle and the three coordinate directions is presented. This new factor brings considerable independence and versatility to radiative transfer analysis as it allows determining the radiative energy for points lying on a plane at an arbitrary position. By virtue of the radiation vector theory, the calculation is performed whether the angles that the plane forms with the coordinate directions are known. If the said plane cuts the disk in two halves a new factor is also presented for the radiant interchange between a half disk and a differential element. Besides, by extension of the case of the circle, the view factor between a sphere and a differential element in a random position is deducted.