Yu Haiyan, Li Mingdong, Guo Ning, Chen Anqi, Zhang Haochun, Du Mu
Institute of Thermal Science and Technology, Shandong University, Jinan 250061, China.
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China.
Gels. 2025 May 26;11(6):391. doi: 10.3390/gels11060391.
The closed mesoporous polymer gels have garnered significant attention as advanced thermal insulation materials due to their superior lightweight characteristics and excellent thermal management capabilities. To accurately predict their thermal performance, this study develops a novel mathematical model that integrates fractal geometry theory, Kirchhoff's thermal conduction principles, comprehensive Rosseland diffusion approximation, and Mie scattering theory. The conductive thermal conductivity component was formulated based on a diagonal cross fractal structure, while the radiative component was derived considering microscale radiative effects. Model predictions exhibit strong agreement with experimental results from various mesoporous polymer gels, achieving a prediction error of less than 11.2%. Furthermore, a detailed parametric analysis was conducted, elucidating the influences of porosity, cell size, temperature, refractive index, and extinction coefficient. The findings identify a critical cell size range (1-100 µm) and porosity range (0.74-0.97) where minimum thermal conductivity occurs. This proposed modeling approach offers a robust and efficient theoretical tool for designing and optimizing the thermal insulation characteristics of closed mesoporous polymer gels, thereby advancing their application in diverse energy conversion and management systems.
由于其卓越的轻质特性和出色的热管理能力，封闭介孔聚合物凝胶作为先进的隔热材料受到了广泛关注。为了准确预测其热性能，本研究开发了一种新颖的数学模型，该模型整合了分形几何理论、基尔霍夫热传导原理、综合罗斯兰扩散近似和米氏散射理论。基于对角交叉分形结构制定了传导热导率分量，同时考虑微观尺度辐射效应推导了辐射分量。模型预测结果与各种介孔聚合物凝胶的实验结果高度吻合，预测误差小于11.2%。此外，进行了详细的参数分析，阐明了孔隙率、孔尺寸、温度、折射率和消光系数的影响。研究结果确定了最小热导率出现时的临界孔尺寸范围（1-100微米）和孔隙率范围（0.74-0.97）。这种提出的建模方法为设计和优化封闭介孔聚合物凝胶的隔热特性提供了一种强大而有效的理论工具，从而推动其在各种能量转换和管理系统中的应用。
