Atroph and I have discussed (and even debated at one point) this topic at length in the RX200 thread we darn near hijacked (my apologies to all for that).
He's won me over and I feel I understand it now.
It's clear to me, based on the math of it, that the TCR of the circuit does "change" (so to speak) with a dual parallel config.
Forget the TCR of a material (which doesn't change), it's the combined circuit as a whole that matters.
As for Heat Flux, it lowers, not raises in a dual coil config.
If you look at the Steam Engine Coil Wrapping tool you can see this in action:
E.g. build: Ti, 28 gauge, Target Resistance .5 ohms (about 8 wraps for single, 16 wraps for dual) has a Heat Flux (how hot it gets) at 30 watts of 345.
Same build (same Target Resistance) in dual coil the Heat Flux drops to 86.
Because the mod doesn't know it's a dual coil, only knows the Target Resistance, it pushes the same wattage in both builds to do its TC thing.
That same wattage on the dual coil, viewed at a whole from the "fooled" mod, ends up reporting back less change in resistance (because the Heat Flux is lower).
Because it's reporting back less change in resistance, it's almost like a new material is present (the "circuit" becomes this new "material" so to speak).
Effectively, the TCR "changes" (from the mod's point of view) when hitting a dual coil at the same Target Resistance.
It's not the material that's changing, it's the parallel (rather than series) circuit.
I made a typo on the heat flux/capacity thing. Heat flux decreases and heat flux increases with both dual coils and lower gauge wire. Resistance increases as the coils heat up, more coil mass means that more power (watts) is needed to reach a certain temperature, meaning a tc mod will push more wattage to a dual coil of equal resistance but double the mass of a single coil. The effective tcr does not change. I don't now what the sc/dc setting does on mods that have it (any others than three xcube?) but it's been theorised that it simply increases the preheat.
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