Thermal conduction of composites with needle-shaped inclusions

In the present work we consider the effective thermal conduction (ϰe)(ϰe) of two-component composites consisting of a matrix with specific thermal conductivity ϰ1ϰ1 and the needle-shaped inclusions with thermal conductivity ϰ2ϰ2. We are particularly interested in the case when ϰ2≫ϰ1, 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 ϰeϰe 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.