I read through this and the engineer in me wanted to investigate some of the simplifications you made so I set out to optimize the HERMs coil analytically.
Over here most people use an AC pump produced by march or chuggar and because the “optimum” length is so dependent on the pump curve I wanted to be able to produce a family of curves for any pump and tubing set up. The example below is for the March 815-SS pump (one of the most common brewing pumps in the US) and assumes you have two 4ft lengths of 1/2" dia silicone hose with 90 elbows and cam lock fittings, a ball valve that is all the way open on your pump, 1/2" OD stainless steel tubing for the coil, and that you can maintain constant temp in your mash tun (i.e. you can provide the same heat you are extracting).
One thing the article neglected is that you don’t necessarily want higher HERMs outlet temps. Heat transfer is maximized when the temperature difference between the two materials is large. What that means is that the closer your wort temp in the HERMs coil gets to the HLT temp the less heat transfer into that fluid you get for the same area of heat exchanger. Additionally they neglect the fact that you don’t want the wort to get above 168F at all or you will start denaturing all of your amylases. On that note, you really want to do all you can to decrease the heat load on those amylases; therefore, you really want to have as small of a HERMs outlet temp differential as possible with a high flow rate.
The first run I just spit out the power vs. coil length but neglected the outlet temp and you get the graph below, which just says you want as big of a temperature difference between your mash temp and the HLT temp with a coil length of about 20ft.
The second run I killed each curve when the outlet temp increased above 165F (74C) which is why you see that strange feather shape on the left. The straight line back to zero is just a bug in how I plotted it, the curve should terminate at the top. What this says is that your maximum “enzyme safe” temp delta is 9C and at that delta T you want about 18ft of coil (yields a flow rate of ~3.5gpm). You can technically get a higher power system with the same pump if you have a very short coil but because that slope is so steep you run the risk of easily mis-estimating the head loss and not getting much power transfer at all or cooking your wort. To me, the risk is not worth the marginal power increase from the 9C delta set up. Also, that would need a very high flow rate and I think that would probably just result in a ton of grain bed settling, restricting your flow and then cooking your wort.
-You don’t need the expensive 50+ foot coils everyone is trying to sell you
-Next time I see an article about brewing that relates to engineering I should probably just not read it for my own sake