A recurrence formula for the prediction of the effective thermal conductivity of fiber reinforced composites with an inhomogeneous interphase

The thermal conductivities of fiber reinforced composites with an inhomogeneous interphase are studied.The inhomogeneous interphase with continuously varied thermal conductivity can be modeled by a multi-layer concentric cylindrical homogeneous shell. The generalized self-consistent method and complex variable technology are applied to obtain an analytical recurrence formula of the effective conductivity. In the cases of the idealized zero thickness interface and homogeneous interphase，the closed form solutions are given by the recurrence formulae. The former has been given by previous researchers. When the volume fraction of fibers is small，the predictions by both models of the idealized zero thickness interface and inhomogeneous interphase and the experiment results are in good agreement，but when the volume fraction of fiber gets large，only the model of inhomogeneous interphase leads to good predictions. The present recurrence formula can also be used to analyze the thermal conductivity of a composite with multi-coating fibers.