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Fully developed flow of granular materials down a heated inclined plane

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Summary

The mechanics of flowing granular materials such as coal, sand, metal ores, etc., and their flow characteristics have received considerable attention in recent years as it has relevance to several important technological problems. In a number of instances, these materials are also heated prior to processing, or cooled after processing. The governing equations for the flow of granular materials, taking into account the heat transfer mechanism by conduction, are derived using a continuum model (cf. Goodman and Cowin [1], [2], Rajagopal and Massoudi [3]). For a fully developed flow of these materials down an inclined plane, the equations reduce to a system of coupled non-linear ordinary differential equations. The resulting boundary value problem is solved numerically and the results are presented for cases where the viscosity and thermal conductivity are assumed to be functions of the volume fraction. It is shown that the equations admit multiple solutions for certain values of the parameters.

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Abbreviations

D :

Symmetric part of the velocity gradient

K :

thermal conductivity

L :

velocity gradient

T :

Cauchy stress tensor

b :

body force

h :

characteristic height

q :

heat flux

r :

radiating heat

u :

velocity vector

α:

angle of inclination of the inclined plane with the horizontal

ɛ:

specific internal energy

γ:

distributed mass density

Θ:

temperature

ν:

volume fraction

ϱ:

bulk mass density

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Author notes

  1. R. Gudhe & K. R. Rajagopal

    Present address: Department of Mechanical Engineering, University of Pittsburgh, 15261, Pittsburgh, PA, USA

  2. M. Massoudi

    Present address: U.S. Department of Energy, Pittsburgh Energy Technology Center, P.O. Box 10940, 15236, Pittsburgh, PA, USA

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    1. R. Gudhe
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    2. K. R. Rajagopal
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    3. M. Massoudi
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    Gudhe, R., Rajagopal, K.R. & Massoudi, M. Fully developed flow of granular materials down a heated inclined plane. Acta Mechanica 103, 63–78 (1994). https://doi.org/10.1007/BF01180218

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