The Temperature Distribution Around a Spherical Particle on a Planar Surface

The solutions for three related boundary value problems in tangent sphere coordinates are presented; two of these problems involve a conducting and a nonconducting sphere on a conducting flat surface when the field at infinity is linear. The third problem describes the potential field around a conducting sphere on an insulating surface where the field at infinity vanishes. Depending on the nature of the problem, either the Laplace equation or the Stokes stream function formalism is used. The integral solutions are rewritten as series expansions, which are numerically easier to evaluate.