A new thermal conductivity relational expression for polymer composites with constructal design fillers

Abstract

Constructal law is usually used to optimize the heat transfer enhancement of fillers. The filler with constructal design is easy to form the heat conductive path, so the composite with constructal fillers has high thermal conductivity. However, existing relational expressions cannot reveal the performance of heat transfer enhancement for constructal fillers. In this work, a new relational expression is established to reveal above coupled mechanism and calculate the thermal conductivity of composite with constructal fillers. The filler shape effect the strengthening mechanism of the thermal conductivity ratio. The critical values of the thermal conductivity ratio are round 150, 300, 600, 700 and 950 for rhombic, elliptical, I shaped, T shaped and rectangular fillers. With the increase of the thermal contact resistance, the thermal conductivity of composite will pass through three typical stages: very slow decrease, sharp decrease, and maintained stability. To improve the thermal conductivity of composite by decreasing the thermal contact resistance should be at the second stage (10−4 < thermal contact resistance <0.2). Meanwhile, the effect of filler shape on the thermal conductivity will be decreased with the thermal contact resistance.