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.
Keywords
imperfect interface, point heat source, image method
