A mixer for this application sounds nearly impossible.  If a mixer cannot be mounted on the top, then the next option is a side-entering mixer on one or both ends.  Such a mixer must have a submerged seal that will tolerate 600 to 700 deg C.  A seal for such high temperatures needs to be cooled and may encounter wear from the waste.  Even a submerged mixer must be selected to avoid interference with the internal heaters.
 
The only other option that seems reasonable is a pumped recirculation loop, withdrawing waste from one end of the tank and returning the flow to the other end.  With that arrangement, additional heating could be provided by a heat exchanger in the recirculation loop.  A pump operating at those temperatures in a waste material is also going to encounter seal problems.


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