Fractal morphology of deposits in heat exchangers and their physical properties

Our fundamental hypothesis in this paper is that aggregated deposits grown on a substrate can be construed as media endowed with fractal properties over a finite range of temporal and spatial scales. We present image analysis of industrial deposits that confirm their fractal morphology and then derive an equation governing the thermal conductivity which displays an explicit dependence on the box-counting fractal dimension. We also study the percolation properties of shuffled Sierpinski carpets (SSC) by developing a real space renormalization group (RSRG) theory approach. The theoretical results are critically discussed with reference to the numerical solution of the steady-state heat equation in simulated fouling material.