Mixing and heat conduction in rotating tumblers

Abstract

Slow granular flows play an important role in industries ranging from food to pharmaceuticals to ceramics. This subject has received much attention in recent literature; however, heat transfer in even the simplest particle flows is poorly understood. Heat transfer depends on the flow of granular materials: the bed conductivity is a function of the (changing) micro-structure; heat redistribution also depends on particle mixing/segregation. In this work, a multi-scale, multi-physics modeling technique, thermal particle dynamics (TPD), is used to examine the interplay between transient heat transfer and particle mixing in rotating tumblers. We study the effect of the mixing rate on the heating rate of the granular material by changing the tumbler cross-sectional shape and operation parameters—rotation rate and tumbler filling level. We use the Péclet number in the granular bed to determine the dominant heating mechanism—conduction or convection—and to predict conditions that will favor more rapid flow of thermal energy in the granular bed. The rate of heat transport is characterized using the Nusselt number and a fluids-inspired relationship correlating this quantity with the Péclet values is attempted. Finally, we use a continuum model to study the relationship between the mixing patterns and temperature contours.