Specularity coefficient (ϕ) and particle–particle restitution coefficient (e) are two important parameters governing the flow physics of dispersed gas-particle flows. In this work, a detailed numerical analysis is carried out to get an insight into the effects of these two parameters in the flow hydrodynamics of dispersed gas-particle flows through horizontal channels. Investigations have also been carried out to find the ϕ-e pair for which the phase velocities become an extremum. It has been found that at a particular value of e, both gas and particle velocities at the centerline of the channel increase with increase in the value of ϕ whereas near the wall, they tend to decrease. At a fixed non-zero value of ϕ both gas and particle velocities tend to increase with increase in the value of e. For ϕ equal to zero, which corresponds to free-slip boundary condition for particle velocity, there is no significant variations in gas and particle velocities with changes in e. Out of all combinations of values of ϕ and e investigated herein, it is found that both gas and particle velocities attain a maximum value when both the values of ϕ and e are maximum. © 2018 The Society of Powder Technology Japan