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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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|
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