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Fractal-Based Thermal Conductivity Prediction Modeling for Closed Mesoporous Polymer Gels.

Haiyan Yu¹, Mingdong Li¹, Ning Guo¹

¹Institute of Thermal Science and Technology, Shandong University, Jinan 250061, China.

Gels (Basel, Switzerland)

|June 25, 2025

Summary

This study presents a new model for predicting the thermal insulation of mesoporous polymer gels. The model accurately predicts thermal performance, identifying optimal ranges for porosity and cell size for enhanced thermal management.

Keywords:

fractal modeling mesoporous polymer gels microscale heat transfer microscale thermal radiation thermal conductivity

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Area of Science:

Materials Science
Thermal Engineering
Applied Physics

Background:

Closed mesoporous polymer gels are advanced thermal insulation materials.
Lightweight characteristics and thermal management are key properties.
Accurate prediction of thermal performance is crucial for material design.

Purpose of the Study:

To develop a novel mathematical model for predicting the thermal performance of closed mesoporous polymer gels.
To integrate fractal geometry, Kirchhoff's principles, Rosseland approximation, and Mie scattering theory.
To analyze the influence of various parameters on thermal conductivity.

Main Methods:

Developed a mathematical model incorporating fractal geometry, Kirchhoff's thermal conduction principles, Rosseland diffusion approximation, and Mie scattering theory.
Formulated conductive thermal conductivity based on a diagonal cross fractal structure.
Derived radiative thermal conductivity considering microscale radiative effects.

Main Results:

Model predictions showed strong agreement with experimental results for mesoporous polymer gels (prediction error < 11.2%).
Parametric analysis revealed the influence of porosity, cell size, temperature, refractive index, and extinction coefficient.
Identified critical ranges for cell size (1-100 µm) and porosity (0.74-0.97) for minimum thermal conductivity.

Conclusions:

The proposed model provides a robust theoretical tool for predicting thermal insulation performance.
The model aids in designing and optimizing mesoporous polymer gels for thermal management.
Findings advance the application of these materials in energy conversion and management systems.