2

where the first term on the right-hand side represents the generation of energy by the solid stress tensor, rs, the second term represents diffusion of energy (ke is the diffusion coefficient). The third term represents collisional dissipation of energy. The fourth and fifth terms represent energy exchange between fluid and solid, and solid and solid respectively. In order to close the equation set, it is necessary to develop expressions for new terms appearing in the governing equation of granular temperature. For these terms as well, several different alternative expressions have been derived (see Gidaspaw, 1994 and a review by Peirano, 1998). Without discussing specific issues related to these different expressions, here we list some of the most commonly used expressions required to close the equation set. Granular temperature conductivity can be written:

75psds.

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