Influence of microstructure size on temperature distribution in biperiodic composite

In this work, the problem of heat conduction in a biperiodic composite consisting of two constituent materials was analysed. To average the discontinuous coefficients in the heat conduction equation, which arise from the heterogeneous structure, the technique of tolerance modelling was applied. The finite difference method was then used to solve the resulting system of equations and to determine the distribution of the unknowns. The finite difference method algorithm was implemented in Maple 2019 software. The main objective of the analysis was to investigate the influence of the composite’s microstructure size on the distribution of the unknowns, facilitated by the tolerance model equations derived through the tolerance modelling technique. The study demonstrated how the number of composite cells, and consequently the cell size, affects temperature values and their fluctuations under selected boundary conditions.