Fractal dimension and time factors of sawdust pattern formation in sawmills

Abstract:

This paper presents the application offractal theory, especially fractal dimension to the formation of sawdust particles during operation with four detailed cases, which helps us to understand the distribution of the sawdust particles inhaled by sawmill workers and remove the effect of toxicity on their body quickly. Pattern of formation of sawdust in human lungs and other parts of the body (in fast branching rate) is described with a practical case study in a developing country. As these sawdust particles settle down in the human body, cells are destroyed on a very fast rate by the toxic nature of sawdust particles. Thus, removing the effect of toxicity on the body will require special skill and is cost intensive. The pattern formation of sawdust particles follows random walking in 2-D Euclidean space using fractal dimension and time steps. Percentage total of average time steps required for aggregation of specified n-sawdust particles varies according to power law of percentage successive aggregation. Case 3 and its rules are the most reasonable if used in a real project since its percentage absolute error compared with the standard literature value of 1.71 is zero. The paper may be of great importance to occupational health scientist and those who control and monitor occupation health problems in small scale industries particularly where occupational hazards are well pronounced.