On some general imperfect interface models for conductivity problem

Three general imperfect interface models for thermal conduction are presented. The discontinuity of the microscopic field is described through the interface parameters: one characterizes the temperature jump, and another controls the heat flux jump. These models include the highly and lowly conducting ones as particular cases. The effective conductivity of composite materials with imperfect interfaces is derived from several effective medium approximations. Unlike the perfect interface, the effective conductivity of a composite containing imperfectly bonded inclusions depends on the size of the particles. The results for these models are illustrated by numerical calculations. Some discussions are also presented.