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Heat and Mass Transfer in Tubes: An Analysis Using the Method of Volume Averaging

Volume 5, Numéro 3, 2002, 18 pages
DOI: 10.1615/JPorMedia.v5.i3.10
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RÉSUMÉ

In this study, we use the method of volume averaging to predict the exchange coefficient associated with steady laminar flow in a tube. This allows us to compare theory with an exact solution. Good agreement is obtained between the theory and the exact solution for the asymptotic condition, and this provides support for the simplifications that are made in the closure problem for transport processes in porous media.

CITÉ PAR
  1. Pierre C., Plouraboue F., Quintard M., Convergence of the Generalized Volume Averaging Method on a Convection-Diffusion Problem: A Spectral Perspective, SIAM Journal on Applied Mathematics, 66, 1, 2005. Crossref

  2. Nakayama A., Kuwahara F., Algebraic model for thermal dispersion heat flux within porous media, AIChE Journal, 51, 10, 2005. Crossref

  3. Upadhyay Virat K., Szymczak Piotr, Ladd Anthony J. C., Initial conditions or emergence: What determines dissolution patterns in rough fractures?, Journal of Geophysical Research: Solid Earth, 120, 9, 2015. Crossref

  4. Soulaine Cyprien, Debenest Gérald, Quintard Michel, Upscaling multi-component two-phase flow in porous media with partitioning coefficient, Chemical Engineering Science, 66, 23, 2011. Crossref

  5. Golfier Fabrice, Quintard Michel, Wood Brian D., Comparison of theory and experiment for solute transport in weakly heterogeneous bimodal porous media, Advances in Water Resources, 34, 7, 2011. Crossref

  6. Davit Yohan, Debenest Gérald, Wood Brian D., Quintard Michel, Modeling non-equilibrium mass transport in biologically reactive porous media, Advances in Water Resources, 33, 9, 2010. Crossref

  7. Orgogozo Laurent, Golfier Fabrice, Buès Michel, Quintard Michel, Upscaling of transport processes in porous media with biofilms in non-equilibrium conditions, Advances in Water Resources, 33, 5, 2010. Crossref

  8. Guo Jianwei, Quintard Michel, Laouafa Farid, Dispersion in Porous Media with Heterogeneous Nonlinear Reactions, Transport in Porous Media, 109, 3, 2015. Crossref

  9. Porta G., Chaynikov S., Riva M., Guadagnini A., Upscaling solute transport in porous media from the pore scale to dual- and multicontinuum formulations, Water Resources Research, 49, 4, 2013. Crossref

  10. Fichot F., Duval F., Trégourès N., Béchaud C., Quintard M., The impact of thermal non-equilibrium and large-scale 2D/3D effects on debris bed reflooding and coolability, Nuclear Engineering and Design, 236, 19-21, 2006. Crossref

  11. Luo Haishan, Quintard Michel, Debenest Gérald, Laouafa Farid, Properties of a diffuse interface model based on a porous medium theory for solid–liquid dissolution problems, Computational Geosciences, 16, 4, 2012. Crossref

  12. Starchenko Vitaliy, Marra Cameron J., Ladd Anthony J. C., Three-dimensional simulations of fracture dissolution, Journal of Geophysical Research: Solid Earth, 121, 9, 2016. Crossref

  13. Ladd Anthony J. C., Szymczak Piotr, Use and misuse of large-density asymptotics in the reaction-infiltration instability, Water Resources Research, 53, 3, 2017. Crossref

  14. Nield Donald A., Bejan Adrian, Heat Transfer Through a Porous Medium, in Convection in Porous Media, 2017. Crossref

  15. Bahar T., Golfier F., Oltéan C., Lefevre E., Lorgeoux C., Comparison of theory and experiment for NAPL dissolution in porous media, Journal of Contaminant Hydrology, 211, 2018. Crossref

  16. Nield Donald A., Bejan Adrian, Heat Transfer Through a Porous Medium, in Convection in Porous Media, 2013. Crossref

  17. Berg Maxime, Davit Yohan, Quintard Michel, Lorthois Sylvie, Modelling solute transport in the brain microcirculation: is it really well mixed inside the blood vessels?, Journal of Fluid Mechanics, 884, 2020. Crossref

  18. Aguilar-Madera C.G., Herrera-Hernández E.C., Espinosa-Paredes G., Neutron diffusion coefficient for disordered arrays of TRISO particles in spherical nuclear fuel, Annals of Nuclear Energy, 146, 2020. Crossref

  19. Ladd Anthony J.C., Szymczak Piotr, Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods, Annual Review of Chemical and Biomolecular Engineering, 12, 1, 2021. Crossref

  20. Yu Liang, Szymczak Piotr, Ladd Anthony J.C., Dissolution of periodic arrays of grains: Upscaling of pore-scale simulations with fast reactions, Chemical Geology, 592, 2022. Crossref

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