Comparative Analysis for Thermal Conductivity Estimates of Unidirectional Fiber Composites

This work is based on the dual variational formulation of the stationary heat conductivity problem for inhomogeneous anisotropic solids. The article offers two-sided estimates for the principal values of the tensor taking into account the mutual arrangement of the anisotropic reinforcing fiber cross-sections in a plane perpendicular to their axes. We considered different types of arrangement of fiber crosssections: the heat conduction composite is transversely isotropic or orthotropic. The estimates we calculated show that there are limits to the possible values of the thermal conductivity tensor components for the composite analyzed. As a result, it is possible to carry out an objective comparative analysis for the calculated ratios obtained using various approaches and intended to determine the desired characteristics. We estimated the most significant margins of error that occur when the target values for each component of the tensor are selected as half-sum of its boundary values. We determined the limits for key parameters that show reliable results with a significant difference in the thermal conductivity of the composite matrix and fibers.

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