Fractal analysis of thermal conduction of loose coal

For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructure by scanning samples with a digital microscope. With the use of Matlab, these gray images were transformed into binary images, which were then transformed into a corresponding matrix consisting only of the values 0 and 1. According to the calculation method of box-counting dimension, we calculated the fractal dimension of the loose coal to be approximately 1.86. The thermal conductivity expressions of loose coal were derived based on the simulation method of thermal resistance. We calculated the thermal conductivity of loose coal by using a fractal model and compared the calculated values with our experimental data. The results show that the test data show an encouraging agreement with the calculated values. Hence fractal theory is a feasible method for studying thermal conductivity of loose coal.