Tolerance averaging and boundary-layer equations for the heat transfer problems in micro-periodic solids

The macroscopic mathematical models of the heat transfer in micro-periodic solids, obtained by the tolerance averaging approach, are represented by the partial differential equation for the averaged temperature field and the system of ordinary differential equations involving time derivatives of certain extra unknown fields which are called internal thermal variables, cf Woźniak (2000). It follows that in the framework of the aforementioned tolerance models the boundary conditions for temperature can be imposed exclusively on the averaged temperature field. The aim of this contribution is to show how the tolerance averaging technique can be extended in order to satisfy the boundary conditions on higher level of accuracy.