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Aaron M. Lattanzi, Christine M. Hrenya, A coupled, multiphase heat flux boundary condition for the discrete element method, Chemical Engineering Journal, Volume 304, 15 November 2016, Pages 766-773, ISSN 1385-8947, http://dx.doi.org/10.1016/j.cej.2016.07.004.

Abstract: Similar to single-phase flows, multiphase systems with a constant heat flux at the wall are common in practice. Unlike single-phase flows, however, the numerical implementation of a constant boundary flux is non-trivial due to the coupling between phases – i.e., the partition of the total flux between the phases can vary in space and time. A numerical technique for modeling such a boundary condition is proposed here and verified via simulations of gas-solid flows. While discrete-particle simulations of monodisperse particles are considered here, the technique can be extended to include radiation, polydisperse systems, and/or a continuum representation of the solids phase.
Keywords: DEM; Heat transfer; Boundary conditions