Abstract
In this study, we developed two frameworks to investigate the thermophoretic particulate deposition in
non-isothermal tube flows conveying particles ranging from 10 to 300 nm; a one dimensional model
where the variables are assumed to be uniform in each cross section perpendicular to the tube axis
and an axi-symmetric model where the aforementioned assumption is relaxed. In the one dimensional
model, the rate of mass deposition along the inner surface of the tube is computed based on the local
thermophoretic velocity of the particulate phase at the wall. This velocity is proportional to the radial
gradient of the temperature at the wall and is calculated via some empirical correlations for heat transfer
in tube flows. In the axi-symmetric model, the rate of deposition is computed through the Fick’s law after
solving the species transport equation for the solid phase. We included the formation of the soot layer
through moving the gas–solid interface in both models. The tube effectiveness (the ratio of actual heat
transfer to the maximum possible heat transfer) decreases due to the formation of the layer. Model outputs
including deposited mass along the tube wall and the tube effectiveness drop have been compared
against experiments. While the computed results through both models agree with the trend of experimental
data, the axi-symmetric results are closer to the experiments in most cases. The calculated deposited
mass is smaller (and closer to experiments) for the axi-symmetric model compared to the one
dimensional model in all cases. This indicates that the axi-symmetric model estimates the deposited
mass more accurately.
