Predicting the effective thermal conductivity of porous building materials using improved Menger sponge fractal structure

Abstract

Accurately obtaining the effective thermal conductivity of porous building materials can correctly understand its thermal insulation performance and ensure the selection of effective building thermal insulation materials, which can bring certain help to building energy conservation. A novel method based on fractal theory combined with the principle of thermoelectric analogy is proposed to predict the effective thermal conductivity of solid-fluid two-phase porous building materials whose solid phase is particles. By improving the fractal structure of the self-similar Menger sponge and considering the incomplete contact form between solid particles inside the characteristic unit, a physical model of heat conduction suitable for porous building materials is obtained. Then, the thermal resistance in the cubic characteristic unit of the improved Menger sponge is calculated using the principle of thermoelectric analogy. Finally, this study obtains a thermal conductivity prediction model that can predict the thermal conductivity of solid-fluid two-phase porous building materials in the full porosity range. The prediction effect of the prediction model is verified when the porosity is 0.55, 0.41, 0.3, and 0.17. The results show that the model is accurate and effective, and the prediction effect is much better than the theoretical prediction models such as series and parallel. And the model has good practicability, which can bring a feasible method for obtaining the effective thermal conductivity of porous building materials.