M. Massoudi et Tx. Phuoc, FLOW AND HEAT-TRANSFER DUE TO NATURAL-CONVECTION IN GRANULAR-MATERIALS, International journal of non-linear mechanics, 34(2), 1999, pp. 347-359
The present study considers an assembly of spherical particles, densel
y packed, between two vertical flat plates which are at different temp
eratures. The flow due to such a temperature difference is investigate
d. The governing equations for the flow of granular materials, taking
into account the natural convection, are derived using a continuum mod
el. For a fully developed flow of these materials, the equations reduc
e to a system of coupled, non-linear ordinary differential equations.
The non-dimensional forms of the equations are integrated numerically.
The results are then presented for volume fraction, dimensionless vel
ocity, and temperature profiles as functions of various dimensionless
parameters representing the following physical meaning: R-1 is the rat
io of the pressure force to the force developed in the material due to
distribution of the void. R-2 is the ratio of the viscous force to th
e gravity force and R-3 is the product of the Prandtl number and the E
ckert number. (C) 1998 Elsevier Science Ltd. All rights reserved.