Thermal Conductivity Of Unsaturated Fibrous Media By Fractal-Monte Carlo Simulations

The effective thermal conductivity of unsaturated fibrous media is simulated by Fractal-Monte Carlo simulations in this work. Based on the probability model and thermal-electrical analogy method, the proposed model of the effective thermal conductivity can be expressed as an explicit function of fractal dimensions, Dt, Df, intrinsic thermal conductivities, ks, kw, kg, the straight capillary length of a unit cell L0, liquid saturation S, pore size λi as well as porosity ϕ. Each parameter of the proposed model has physical meaning and the function has no empirical constant. The results calculated by Fractal-Monte Carlo simulations have been compared with the experimental data available, and an excellent agreement has been shown for an appropriate range of porosity except for the condition at a lower liquid saturation. It is found that, when ks/kg > 1 and kw/kg > 1, the dimensionless effective thermal conductivity of unsaturated fibrous media decreases with increment in fractal tortuosity dimension and porosity and decrement in liquid saturation. On the other hand, when ks/kg < 1 and kw/kg < 1, the correlations are opposite. The present Fractal-Monte Carlo technique may have its own advantages in predicting other transports in unsaturated fibrous media.