A one-dimensional, two-fluid model has been developed assuming gas phase to be ideal, particles to be spherical and only momentum and heat interaction takes place between gas and particles. Heat transfer between wall and particles, electrical forces, surface tension forces, Saffman lift forces, Magnus forces and capillary forces are neglected.
Due to dilute nature of flow, particle–particle interaction and contribution of pressure gradient to solid phase
momentum are neglected. Accordingly, the governing equations (Eqs. (1), (2), (3) and (4)) for gas and solid phases are
as follows.