Theoretical Investigation on Effective Thermal Conductivity of a Disk-Shaped Composite System

This paper addresses the methodology to estimate the effective thermal conductivity of the wiring board, where the metal wiring network is very complicated and then the thermal conductivity of the metal wiring is more than 1000 times higher than that of the resign board. Based on the concept of analogy between the electric and the thermal resistance network, two types of estimation equations are derived by dividing the composite system parallel or perpendicular to the heated/cooled surface. When the ratio of higher to lower thermal conductivities is less than 10, the estimated values by these equations agree with each other. However, the difference is clearly found between them when the ratio is larger than 100. The estimated values are moreover compared with the exact solutions, which are obtained by numerical simulation of heat transfer using Microsoft Excel, and then the applicability of the present estimation methodology is discussed. It is found that the thermal resistance network obtained by dividing the composite system perpendicular to the heated/cooled surface is effective to estimate the effective thermal conductivity of the composite system.