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A novel method for the calculation of friction factors through the computation of the irreversibility and rate of entropy production in two-phase flows has been developed. The model uses the momentum equation of the twophase fluid as well as appropriate closure equations to compute energy dissipation in a cylindrical pipeline system, which carries an air–solids mixture. Integral flow quantities, such as the total volumetric flow rate of the gas, the solids loadings, the pressure drop, and the friction factor of the flowing mixture may be readily computed from this model. The friction factors obtained via the entropy production method agree very well with experimental data and correlations derived in the past. The calculations also extend to the sources of irreversibility and the rate entropy production due to the friction of the flow as well as to the holdup of the two phases.

Entropy Production, Friction Factors, and Holdup in Particulate Two-Phase Flow in Pipes