Gravity-Driven Granular Flows of Smooth, Inelastic Spheres Down Bumpy Inclines

We employ a kinetic constitutive theory that includes the effects of particle transport and collisions to analyze steady, fully developed, gravity-driven flows of smooth, inelastic spheres down bumpy inclines. By replacing the solid fraction by its depth-averaged value wherever it occurs in the balance equations, we obtain a closed-form solution for the granular temperature profile, which when employed in the constitutive relations for the normal and shear stresses determines the solid fraction and mean velocity profiles. The solutions ensure that the stresses and energy flux vanish at the free surface and that the balance of momentum and energy are satisfied at the base. We also determine for fixed flow rates the ranges of inclinations within which steady flows are possible, and for fixed inclinations the depths of the resulting flows. Most striking are the inclinations and flow rates at which both a dilute, fast flow and a dense, slow flow are possible.