Effect of cylindrical fibers, with cross-sections formed by two circular arcs, on the overall conductivity of a composite

An analytic solution for the steady-state temperature distribution in an infinite conductive medium, containing non-conductive fiber with the cross-section of irregular shape formed by two circles, and subjected to remotely applied uniform heat flux is obtained. The temperature flux on the surface of the inhomogeneity is then determined as a function of the geometrical parameters. This result is used to calculate resistivity contribution tensor for the fiber and to evaluate effective conductive properties of a material containing multiple inhomogeneities of this shape.