You can have steady flow in a plug flow reactor, but that may not be a steady state process due to the reactions that may be going on.

Good Luck,
Latexman

A lot of industrial cooling loops are setup as combinations of steady-state, steady-flow, and shift between at various stages of their process. A strict definition might say it is never steady in either regard, but for the purposes of analysis a stretch of several hours with unchanging conditions is likely steady enough. Or the same loop can be designed a multitude of ways depending on the particular arrangement, operating method, existing equipment, plant needs, etc.

A water cooled air compressor usually receives steady flow. It cycles on and off as needed to fill a reservoir or for use by the plant. If it runs for 15 minutes on, 15 minutes off, all day long, this loop may be best analyzed as steady flow, non-steady state. Hook the same compressor to a large accumulator tank and it now runs for several hours at a time so it may be better analyzed as steady flow, steady state, and the non-load times ignored. It might be equipped with a variable speed booster pump as part of a central cooling system and the loop is only at full flow when the compressor is running in short intervals, which becomes non-steady state, non-steady flow (or very short steady intervals).

Just pulled out the ol' Thermodynamics book. They associate steady-flow with fluid movements and steady-state with thermal changes. More specifically, there are steady-state problems that do not involve flow at all (radiation, conduction problems) and also fluid dynamics problems where thermal changes are insignificant.