FLOW AND HEAT-TRANSFER DUE TO NATURAL-CONVECTION IN GRANULAR-MATERIALS

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.