Prediction of the solid effective thermal conductivity of fatty acid/carbon material composite phase change materials based on fractal theory

Highlights: • Equivalent model of typical Sierpinski carpet is firstly proposed. • General solutions of typical Sierpinski carpet structures are derived. • Model can predict the effective thermal conductivity of composite PCMs. • Proposed prediction model shows a good reliability and high accuration. -- Abstract: The thermal conductivity of a phase change material (PCM) is an important parameter that affects the heat transfer characteristics of PCM. In this study, the fractal theory is conducted to study the prediction model of the effective thermal conductivity of fatty acid/carbon material composite PCMs in the solid phase. Based on the Sierpinski carpet model of fractal geometry, a series of fractal units with different fractal dimensions are developed for the fatty acid/carbon material composite PCMs. Combined with a self-similar principle and thermal resistance network theory, a general solution for the dimensionless effective thermal conductivity of a typical Sierpinski carpet fractal unit is then derived. Further, dimensionless effective thermal conductivity prediction models of three typical structures of fatty acid/carbon material composite PCMs are obtained by comparing the experimental data. Finally, the thermal conductivity prediction model from this study demonstrated a better reliability than that of the commonly used QP prediction model and Maxwell-Eucken prediction model. This prediction model could be used to predict the effective thermal conductivity of composite PCMs.