A Thermophoretic Sherwood Number for Characterizing Submicron-Particle Mass Transfer in Laminar Wall-Bounded Flows

Abstract

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 field and the temperature and particle concentration profiles can be described by their constantproperty 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 particleconcentration 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.

Accuracy in Numerical Solution of the Particle Concentration Field in Laminar Wall-Bounded Flows with Thermophoresis and Diffusion

“…Walker et al (1979) carried out an incompressible analysis of the entrance region of a pipe flow that included an asymptotic treatment of the surface diffusive sublayer, and made Lagrangian calculations of deposition efficiency in the developed downstream region. Brereton and Mehravaran (2013) presented series solutions for submicronparticle concentration profiles in fully-developed laminar pipe and channel flows, and introduced a thermophoretic Sherwood number to characterize the effectiveness with which temperature difference drives particulate mass transport. In each of these studies, emphasis was placed on the extreme thinness, at high particle Schmidt numbers, of the surface sublayer within which effects of Brownian diffusion are present and which accommodates a particle-concentration boundary condition applied at the surface.…”