New solutions to the Eulerian particle-transport equations are presented which describe concentration profiles in wall-bounded, submicron-particle-laden, one-way coupled flows of gases undergoing advective transport and thermophoresis. These solutions have been deduced for the cases of steady, fully developed, laminar flow of hot gas within pipes and channels with a cold surface at a uniform temperature, when the velocity held and the temperature and particle concentration profiles can be described by their constant-property forms. They are used to show how the effectiveness with which temperature difference drives particulate mass transport can be characterized by a dimensionless mass-transport coefficient or thermophoretic Sherwood number—the product of a particle-concentration ratio and the heat-transfer Nusselt number—that is useful in making engineering predictions of and comparisons between particulate mass transfer rates in different flows. The solutions also reveal how the concentration profiles in pipe and channel flows undergo inversion during development, changing from low concentrations near the cold surface and high concentration in the bulk flow near the entrance, to low concentrations in the bulk and high ones near the cold surface when the concentration field has developed fully.
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