Effective thermal conductivity of ceramic blocks with inner ducts

The joint work with Valery Grikurov on thermal conductivity is recollected. This article has been written by one author only (S.Yu.S) but he dared to do it taking into account two reasons Firstly, it gives him the opportunity to recollect his scientific and human communications with late Valery Grikurov. Secondly, it permits him to discuss on an informal level how local characteristics of a media can be generalized to global characteristics of an element. This discussion also can be extended to diffraction problems.