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Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Jyotsna, R and Rao, Kesava K (1991) Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem. In: Chemical Engineering Science, 46 (8). pp. 1951-1967.

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Official URL: http://dx.doi.org/10.1016/0009-2509(91)80156-S

Abstract

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Item Type: Journal Article
Additional Information: copyright of this article belongs to Elsevier science.
Department/Centre: Division of Mechanical Sciences > Chemical Engineering
Date Deposited: 30 Nov 2010 13:15
Last Modified: 30 Nov 2010 13:15
URI: http://eprints.iisc.ernet.in/id/eprint/34142

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