Tolerance modelling of heat conduction in biperiodic fourth-component composite

The object of analysis is a heat conduction problem within the framework of tolerance modelling in fourth-component biperiodic composite. Two materials are isotropic and two are orthotropic, and additionally symmetry axes of orthotropic ones are rotated with respect to each other by an angle equal 90°. The results of some special boundary conditions for stationary problem of heat conduction were obtained from the local homogenization model (LHM). The model equations were derived by simplifying the equations of the standard tolerance model (STM), which were obtained based on two model assumptions: micro-macro decomposition of the temperature field and residual function averaging, after introducing the concept of “weakly slowly varying function” (WSV) and “slowly varying function” (SV) into the modelling process. The presented examples show the influence of the given boundary conditions on the macro-temperature distribution and on the distribution of the approximate temperature field θ(·). The effect of thermal conductivity of the component materials and the number of periodicity cells on temperature distribution was also shown.