Granular flows, wall boundary

Jenkins JT (1992) Boundary Conditions for Rapid Granular Flow Flat, Frictional Walls. J Appl Mech - Trans ASME 59 120-127... 

Modeling Heat Transfer Thermal particle dynamics (TPD) primarily introduced by Vargas and McCarthy [14] incorporated both the contact mechanics and contact conductance theories to model the flow dynamics and heat conduction through dry granular materials. The details of the model can be found in Sahni et al. [12]. Heat transport is simulated accounting for the initial material temperature, wall temperature, heat capacity, heat transfer coefficient, and flow properties using a linear model. The flux of heat transported across the mutual boundary between two particles i and j in contact is described as follows ... 

In Fig. 3, the energy lost due to inelastic collisions and viscous gas are compared. For a mixture flow, compared with inelastic dissipation, the viscous dissipation is relatively small, especially in the region near the boundary wall. Hence it may be acceptable to neglect the effect of the drag force in establishing the boundary conditions. When the granular temperature decreases, the viscous dissipation becomes more important until it is, indeed, greater than the inelastic collision dissipation. 

Jenkins, J. T. 2001. Boundary conditions for collisional grain flows at bumpy, frictional walls. In Granular Gases, edn. T. Poschel and S. Ending, 125-138, Berlin, Germany Springer. 

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