Improving the Sierpinski carpet model arithmetic to accurately predict the thermal conductivity of fatty acid/carbon composite phase-change materials

Abstract

The effective thermal conductivity is an important physical parameter of composite phase-change materials (PCMs). In this study, a new analytic expression of the dimensionless thermal conductivity is proposed to predict the dimensionless thermal conductivity of fatty acid–carbon materials composite PCMs based on the Sierpinski carpet model and the thermal resistance network model of a fractal geometry combined with the principle of the weighted average. The new analytical expression can be used to overcome the issue of the predicted values deviating considerably from the experimental results when the fractal series n is too small. At the same time, an accurate solution for the dimensionless ratio (t+) of the width of the carbon materials to the side length of the Sierpinski carpet is presented. Compared with the general solution algorithm proposed by Song, the commonly used quadratic parallel (QP) prediction model, and the Maxwell–Eucken model, this algorithm is more reliable. The proposed prediction model can be used to predict the effective thermal conductivity of fatty acid–carbon materials.