THERMAL CONDUCTIVITY OF UNSATURATED FIBROUS MEDIA BY FRACTAL-MONTE CARLO SIMULATIONS

Abstract

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, [Formula: see text], [Formula: see text], intrinsic thermal conductivities, [Formula: see text], [Formula: see text], [Formula: see text], the straight capillary length of a unit cell [Formula: see text], liquid saturation [Formula: see text], pore size [Formula: see text] as well as porosity [Formula: see text]. 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 [Formula: see text] and [Formula: see text], 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 [Formula: see text] and [Formula: see text], the correlations are opposite. The present Fractal-Monte Carlo technique may have its own advantages in predicting other transports in unsaturated fibrous media.