The purpose of this work was the direct numerical simulation of heat and fluid flow by granular mixing in a horizontal rotating kiln. To model particle behaviour and the heat and fluid flow in the drum, we solve the mass conservation, momentum and energy conservation equations directly on a fixed Eulerian grid for the whole domain including particles. At the same time the particle dynamics and their collisions are solved on a Lagrangian grid for each particle. To calculate the heat transfer

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... de the particles we use two models: the first is the direct solution of the energy conservation equation in the Lagrangian and Eulerian space, and the second is our so-called linear model that assumes homogeneous distribution of the temperature inside each particle. Numerical simulations showed that, if the thermal diffusivity of the gas phase significantly exceeds the same parameter of the particles, the linear model overpredicts the heating rate of the particles. The influence of the particle size and the angular velocity of the drum on the heating rates of particles is studied and discussed.