Estimation of Transverse Thermal Conductivity of Doubly-periodic Fiber Reinforced Composites

For steady-state heat conduction, a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodicity of the heat flux fields. Then by combining with the eigenfunction expansion of complex potential which satisfies the fiber-matrix interface conditions, an eigenfunction expansion-variational method(EEVM) based on a unit cell is developed. The effective transverse thermal conductivities of doubly-periodic fiber reinforced composites are calculated, and the first-order approximation formula for the square and hexagonal arrays is presented, which is convenient for engineering application. The numerical results show a good convergency of the presented method, even though the fiber volume fraction is relatively high. Comparisons with the existing analytical and experimental results are made to demonstrate the accuracy and validity of the first-order approximation formula for the hexagonal array.