The microscopic conduction fields in the multi-coated sphere composites under the imposed macroscopic gradient and flux fields

Explicit analytical expressions of the microscopic conduction (gradient or flux) fields in the d -dimensional ( d = 2 , 3 ) multi-coated sphere assemblages under the imposed macroscopic gradient and flux fields are presented. Limiting procedures are developed to derive the results for most important specific composites, which include the inclusion composites with highly conducting imperfect interface, lowly conducting (with Kapitza resistance) imperfect interface, general imperfect interface, and those with anisotropic coatings. When the volume proportion of the outermost shells of the assemblages approaches 1, the simplified results for the dilute suspensions of the complex spherically symmetric inclusions in a major matrix are deduced.