Frictional and heat transfer characteristics of flow in square porous tubes of wall-flow monoliths

In the 1D modeling of flow in the channels of wall-flow monoliths used in diesel particulate filters for engine exhaust emissions control, it is common to use friction coefficients and Nusselt numbers from idealized 2D/3D channel flows with zero wall flow. This practice implicitly makes the additional approximation that the actual velocity and scalar (temperature or species concentrations) profiles within the channels are little affected by nonzero wall flow. There is extensive related research in the filtration literature for the simpler geometries of circular tubes and parallel planes that exposes much more complex and interesting effects as the wall Reynolds number, Re-w, increases. Here we extend these results to the 3D geometry of square channels appropriate for wall-flow monoliths. We solve for the fully developed laminar flow, and heat transfer, within long square channels with porous walls and uniform wall velocity. Results are generated for the appropriate parameter range applicable for the diesel particulate filter application which provide the corrected friction coefficients and Nusselt numbers for nonzero Re-w. Furthermore, we confirm the observation, from prior work on the simpler geometries that there exists a limiting Re-w, beyond which there is no fully developed flow for the inlet channels (wall suction). Implications for modeling diesel particulate filters are discussed. (C) 2012 Elsevier Ltd. All rights reserved.