Estimation of Thermal Conductivity of the Fibrous Composite with Continuous Variation in the Thermal Conductivity of the Intermediate Later between the Fiber and Matrix

Composites are widely used as constructional and functional materials in various instrument devices. A significant amount of works is devoted to research of thermal conductivity of composites. However the calculation formulas in these works are derived, as a rule, either as a result of processing of experimental data with reference to specific materials, or by a priori setting of the temperature and heat flow distributions in models of heterogeneous body structures. A mathematical model of thermal energy transfer in the composite reinforced with sufficiently long anisotropic fibers oriented in one direction is offered taking into account the possibility of an intermediate layer occurred between the fibers and the matrix, whose thermal conductivity varies continuously across the thickness.

Based on this model, the formulas for calculating the effective thermal conductivity coefficients of this composite are deduced. The dual variational formulation of the stationary thermal conductivity problem was applied for estimating a possible error of obtained results. The results can be used to predict the effective thermal conductivity coefficients of fibrous composites.

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