Entropy Balance of Steady, Quasi-One-Dimensional, Internal Compressible Flow with Area Change, Heat Addition, and Friction (edited)

The quasi-one-dimensional entropy transport equation is derived for flow with an arbitrary combination of area change, heat transfer, and friction. Irreversibilities are identified using the Clausius-Duhem inequality, which is found to be satisfied in a weak sense. Irreversibility arises due to the difference between a "thermal work" term and reversible work. A closed-form equation is derived in order to calculate the contributions of the individual components to the overall entropy change. Further, a new mechanism is identified, which explains the ability of a discontinuity to generate entropy (e.g., shockwaves in an inviscid and non-thermally conducting fluid). These entropy generation mechanisms are then examined for the "classical" compressible flows: isentropic flow, Rayleigh flow, Fanno flow, and flow across a normal shock. Further, these mechanisms are also used to show entropy generation for sudden expansion, sudden contraction, simultaneous area change with friction and simultaneous heat transfer with friction.