Abstract
In the present work we consider the effective thermal conduction ( ϰ e ) of two-component composites consisting of a matrix with specific thermal conductivity ϰ 1 and the needle-shaped inclusions with thermal conductivity ϰ 2 . We are particularly interested in the case when ϰ 2 ≫ ϰ 1 , and the aspect ratio (length/diameter) of inclusions is also great. Two methods were used to solve the task, first – qualitative analysis based on the diffusion analogy, and second – effective medium approximation, the latter is valid in the wider range of volume fraction of inclusions. Both methods give an upper limit for ϰ e because of idealized approximations made. The developed approach is also suitable for electro-conduction, dielectric permeability, stationary diffusion and other problems with mathematical formulation identical to the considered problem of thermal conduction.
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