Investigating Thermal Insulation in Bio-Derived Cellulose Fiber Reinforced Aerogels: Microscale Modeling and RSM Optimization Approach

Cellulose fiber reinforced aerogel (CFRA) composites are emerging as sustainable super-insulating materials by integrating bio-based cellulose fibers within a silica aerogel matrix, which enhances structural stability while maintaining low thermal conductivity (TC). This study presents a computational framework that predicts and optimizes the effective thermal conductivity (ETC) of CFRA composites using a combination of micromechanical modeling and statistical analysis. A three-dimensional periodic representative volume element (RVE) was developed to simulate steady-state heat conduction, and a Box–Behnken design (BBD) with Response Surface Methodology (RSM) was implemented to model the impact of microstructural parameters. The predictive model, validated against analytical and experimental data, demonstrated excellent accuracy, with a coefficient of determination R² = 0.9976, adjusted R² = 0.9948). Sensitivity analysis revealed that temperature and aerogel TC are the predominant factors influencing ETC, while fiber radius has minimal effect within the studied range (< 0.1% variation). An optimal configuration with a fiber radius of 7 µm, fiber volume fraction of 1.3%, and aerogel conductivity of 0.016 W·m - ¹·K - ¹, yielding an ETC of 0.0163 W·m⁻¹·K⁻¹ at room temperature, which is 37% lower than the TC of air (0.026 W·m⁻¹·K⁻¹). This integrated modeling-optimization framework offers an effective tool for designing and optimizing sustainable CFRA insulation materials.