Abstract
We first phrase a boundary-value problem for a dense, steady, fully-developed, gravitational flow of identical inelastic spheres over in inclined bumpy base in the absence of sidewalls. We then obtain approximate analytical solutions for the profiles of the solid volume fraction, the strength of the velocity fluctuations, and the mean velocity of the flow. We compare these with those obtained in numerical solutions of the exact equations.
Highlights
Flows of granular materials down inclines occur often in Nature and in industry
We employ extended kinetic theory to phrase a boundary-value problem for the variations of these fields across the flow and obtain approximate, analytical solutions for them that we compare to numerical solutions of the exact equations
In the expressions for the stress, we retain only terms that result from collisional transfer of momentum and ignore those that result from transport
Summary
It is important to be able to describe and predict them Because such flow take place under the influence of gravity, they typically involve solid volume fractions greater than 0.30. The predictions for the properties of inclined flow fail, and alternatives must be employed. The two approaches have much in common [10, 11] We employ the latter to phrase a boundaryvalue problem for a dense, steady, fully-developed, gravitational flow of identical inelastic spheres over an inclined bumpy base in the absence of sidewalls. We employ extended kinetic theory to phrase a boundary-value problem for the variations of these fields across the flow and obtain approximate, analytical solutions for them that we compare to numerical solutions of the exact equations
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