Yeah, I think if we had a defined system it would be clear. Say two atmospheric tanks, one with a water level 10m below the other. All parallel pipes between these tanks (with submerged entrances and exits) would have a head loss of 10m regardless of how many pipes you put in.
But isn't head loss analogous to voltage drop? Parallel resistors have the same voltage drop.
This assumes the parallel pipes have entrances that are all in the same vessel at the same elevation to each other, and the exits are all in another vessel at the same elevation to each other.
I'd...
First, clearly define variables:
TA, TB, Tf, C=mc as above.
Ta = variable temperature of tank A.
Tb = variable temperature of tank B.
QA = variable heat leaving tank A and entering engine.
QB = variable heat leaving engine and entering tank B.
W = variable work produced by engine.
We know the...
A note on the "10% loss."
Since we don't know exactly where the heat loss occurs, it is prudent to consider it to occur after the heat is transferred through the tubes. (Prudent because it results in 10% greater surface area and is thus more conservative.)
That is why I would not incorporate...