The Effect of a Correlated Surface Roughness and Convection on Heat Conduction
Heat conduction through a slab, 0 ≤ x ≤ W is one dimensional. However, if one of the edges, say x=0, is rough the conduction will be two dimensional. The two dimensionality varies with the correlation length with a maximum at a length approximately 10% of the slab width. The maximum percentage standard deviation of the flux is of the order of 3 time that of the roughness. Monte Carlo simulation, while expensive, proved to be the best approach. This was particularly true because of the high efficiency of the mesh generator and solver in COMSOL.