3D Green’s functions for a steady point heat source interacting with a homogeneous imperfect interface

The image method is applied to derive the three-dimensional temperature field induced by a steady point heat source interacting with a homogeneous imperfect interface.Our approach is a straightforward extension of that of Sommerfeld who addressed the half-space Green's function for a steady point heat source at the beginning of the last century.Both weakly and highly conducting type imperfect interface conditions are considered.It is found that the temperature field for both types of imperfect interface is only dependent on the two-phase conductivity parameter and another parameter measuring the interface "rigidity".As an application, we discuss the Coulomb force on a static point electric charge due to its interaction with the imperfect interface.It is possible to find an equilibrium position for the electric charge interacting with an imperfect interface.In addition, the equilibrium position is stable provided the interface is weakly conducting whereas the equilibrium position is unstable if the interface is highly conducting.