THE GENERAL-SOLUTION AND FAXEN LAWS FOR THE TEMPERATURE-FIELDS IN AND OUTSIDE AN ISOLATED ELLIPSOID

The image systems for the disturbance temperature fields in and outside an isolated ellipsoid driven by an n-th order ambient field are introduced and their connection to the ellipsoidal harmonics is derived. More general ambient fields may be handled by superposition of these basic solutions. These results have been used to derive the Faxen relation for the arbitrary n-th order multipole moment. The explicit expressions for the temperature fields and the thermal moment tensors for an ellipsoid in linear and quadratic ambient fields are given to illustrate the method.