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Heat and momentum transfer to a particle in a laminar boundary layer

Published online by Cambridge University Press:  24 February 2020

Aaron M. Lattanzi Open the ORCID record for Aaron M. Lattanzi [Opens in a new window] ,
Xiaolong Yin  and
Christine M. Hrenya
Aaron M. Lattanzi
Affiliation:
University of Colorado at Boulder, Department of Chemical and Biological Engineering, Boulder, CO, USA
Xiaolong Yin
Affiliation:
Colorado School of Mines, Petroleum Engineering, Golden, CO, USA
Christine M. Hrenya*
Affiliation:
University of Colorado at Boulder, Department of Chemical and Biological Engineering, Boulder, CO, USA
*
†Email address for correspondence: hrenya@colorado.edu
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Abstract

Bounding walls or immersed surfaces are utilized in many industrial systems as the primary thermal source to heat a gas–solids mixture. Previous efforts to resolve the solids’ heat transfer near a boundary involve the extension of unbounded convection correlations into the near-wall region in conjunction with particle-scale theories for indirect conduction. Moreover, unbounded drag correlations are utilized in the near-wall region (without modification) to resolve the force exerted on a solid particle by the fluid. We rigorously test unbounded correlations and indirect conduction theory against outputs from direct numerical simulation of laminar flow past a hot plate and a static, cold particle. Here, local variables are utilized for consistency with unresolved computational fluid dynamics discrete element methods and lead to new unbounded correlations that are self-similar to those obtained with free-stream variables. The new drag correlation with local fluid velocity captures the drag force in both the unbounded system as well as the near-wall region while the classic, unbounded drag correlation with free-stream fluid velocity dramatically over-predicts the drag force in the near-wall region. Similarly, classic, unbounded convection correlations are found to under-predict the heat transfer occurring in the near-wall region. Inclusion of indirect conduction, in addition to unbounded convection, performs markedly better. To account for boundary effects, a new Nusselt correlation is developed for the heat transfer in excess of local, unbounded convection. The excess wall Nusselt number depends solely on the dimensionless particle–wall separation distance and asymptotically decays to zero for large particle–wall separation distances, seaming together the unbounded and near-wall regions.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Granular media: Granular media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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