I think I already know the answer to this question is "It does not

I think I already know the answer to this question is “It does not matter”, but … Does the direction of water flow matter as to which is input and which is output?

I don’t see how but then again I could not see how the conductivity of the coolant mattered !
I have heard some say it does …

I’d make the HV end the “cold” end. But who knows if it really matters, dunno.

wild and unfounded thoughts maybe it matters due to the temp difference and stress from the differential?

In water to water heat exchangers it very important, they need to be cross flow, ie flow from the left exchanger plates flows into flow going right on the opposite excganger. For this application not sure which side is hotter the cathode or anode?

@Abe_Fouhy mmmm, I think the cathode is hotter but that is a good question. An item to measure I guess :).