Fractal Analysis of Effective Thermal Conductivity for Woven Fabrics used in Fire Fighters’ Protective Clothing

Abstract

Radiation heat transfer within the fabric used in fire protective clothing is one of the critical factors affecting thermal protective performance under simulated fire. In the present article, a fractal analysis of effective thermal conductivity for flame-resistant fabric is presented based on the thermal-electrical analogy and statistical self-similarity of yarns within fabric. The thermal radiation influence is considered in the fractal model. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macropores (gaps or channels) between the yarns and micropores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. It was found that the calculated results corresponded well with the experimental data within an average of. 4.9% at mean tested temperature of 200°C. This confirms the good behavior of the model and the validity of results. Thermal conductivity values increased for fabric under high temperature as mean test temperatures are increased due to the nonlinear nature of radiation heat transfer.