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Title: Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems

Abstract

We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.

Authors:
;
Publication Date:
Research Org.:
National Energy Technology Laboratory (NETL), Pittsburgh, PA, Morgantown, WV, and Albany, OR (United States)
Sponsoring Org.:
USDOE - Office of Fossil Energy (FE)
OSTI Identifier:
912705
Report Number(s):
DOE/NETL-IR-2007-031
TRN: US200801%%981
DOE Contract Number:  
None cited
Resource Type:
Journal Article
Journal Name:
Mathematical Problems in Engineering
Additional Journal Information:
Journal Volume: 2006; Journal Issue: aritcle ID 56046; Related Information: This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Publisher:
Hindawi Publishing Corporation
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; BOUNDARY-VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; DIMENSIONLESS NUMBERS; GRANULAR MATERIALS; HEAT TRANSFER; SOLIDS FLOW; NONLINEAR PROBLEMS

Citation Formats

Massoudi, M C, and Tran, P X. Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems. United States: N. p., 2006. Web. doi:10.1155/MPE/2006/56046.
Massoudi, M C, & Tran, P X. Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems. United States. https://doi.org/10.1155/MPE/2006/56046
Massoudi, M C, and Tran, P X. 2006. "Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems". United States. https://doi.org/10.1155/MPE/2006/56046. https://www.osti.gov/servlets/purl/912705.
@article{osti_912705,
title = {Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems},
author = {Massoudi, M C and Tran, P X},
abstractNote = {We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.},
doi = {10.1155/MPE/2006/56046},
url = {https://www.osti.gov/biblio/912705}, journal = {Mathematical Problems in Engineering},
number = aritcle ID 56046,
volume = 2006,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
}

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