The first things to determine is the required heat transfer rate. I.e The desired flow rate - at some low enough flow rate the system will work, but you need to make it work at the flow rate you require.
Chem. Engineering guys are really into this stuff and I know that being able to scale up from a trial plant to a production plant (usually correctly) is one of their skills.
There are three heat transfer mechainisms: into the water (force convection), through the copper and out of the heat bank (natural convection).
The only one which I think you can easily find out about at a theoretical level is the heat through the copper.
As a guide I would say from experience 2/3 of standard cylinder (115 litres?) is heated from 20 to 60 by water at 70in - 55 out in 20 minutes through a coil of 5 turns of 300mm diam made from 22mm copper pipe.
My guess is that the natural convection is perhaps the bottle neck? I.e. the outside of the copper tube is about the same as the fluid inside. This is likely to be more than proportionately the problem when scaling down.
Another way of looking at it is to say if the water travelled at 1 m/s in the 10mm tube it would be subjected to 25s of heating - how hot would it get in that time - intuitively I'd guess pretty much the same as the heat store.
This is just some interesting thinking aloud.
I'll be fascinated with the results.