Joseph Meehan wrote:

What exactly is a contra-flow heat exchanger?

In a counterflow heat exchanger, hot and cold fluids flow in opposite
directions. If 100 F greywater flows into one end of a pipe and 60 F
fresh water flows into the other end of a tube inside the pipe with equal
flow rates C Btu/h-F and heat transfer area A in ft^2 and conductance
U Btu/h-F-ft^2, NTU = AU/C, E = NTU/(NTU+1), which can be very close
to 1 with large areas and low flow rates, ie close to 100% efficiency,
vs 50% max for a parallel flow exchanger with both fluids flowing in
the same direction.

We might drip 50 gallons per day (C = 50x8.33/24h = 17 Btu/h-F) into
a 1.25"x100' plastic pipe around a 3/4" tube with A = 100Pix3/4/12
= 19.6 ft^2 and U = 10 Btu/h-F-ft^2 and NTU = 19.6x10/17 = 11.5 and
E = 11.5/12.5 = 0.92, ie 92% efficiency. With 200' of pipe, E = 96%.

... How is it powered?

It isn't, other than some way to make the fluids move, eg gravity for
greywater and thermosyphoning for fresh water, in a vertical version.

Nick