Heat transfer in polymer composites filled with inorganic hollow micro-spheres: A theoretical model

The heat transfer mechanisms in inorganic hollow micro-spheres filled polymer composites are analyzed in the present paper. This heat transfer includes mainly three mechanisms: (1) thermal conduction between solid and gas; (2) thermal radiation between the hollow micro-sphere surfaces; and (3) natural thermal convection of the gas in the micro-hollow spheres. A theoretical model of heat transfer in polymer/inorganic hollow micro-sphere composites is established based on the law of minimal thermal resistance and the equal law of the specific equivalent thermal conductivity, and a corresponding equation of effective thermal conductivity is derived. The effective thermal conductivity (k_eff) of hollow glass bead-filled polypropylene composites is estimated by using this equation, and is compared with the numerical simulations by means of a finite element method. The results show that the variation of the theoretical estimations of k_eff are similar to the numerical simulations at lower filler volume fraction (φ_f20%). Moreover, k_eff decreases linearly with increasing φ_f, and reduces somewhat with increase of filler size.