I've had two cookstoves with connected hot water systems; supplied us with all the hot water needed for seven years living off the grid. Next seven years we ran a "bread-box" solar water heater in the summer and the wood stove water heater in the winter. The principle of operation is thermo-siphon; heat rises.
With a thermo-siphon system the opposite of "heat goes up" is "cool goes down". In use, water is circulated in a "loop" powered by the heat source, in this case the burning wood. As the water in the firebox coil heats it rises and is deposited in the top of a storage tank. Since this is a "closed convection loop" the water in the firebox coil is replaced with the cooler water from the bottom of the tank. As long as the firebox has wood burning this convection cycle continues. The water drawn in may be warm but the firebox is hotter so the cycle continues.
It can take a couple of hours before the tank has heated one cycle. This may be plenty warm enough for dishes and laundry. For bathing you may need a couple of cycles. After several cycles the water can get very hot but it never blew off a conventional temperature/pressure relief valve even though the cooksove sometimes ran 24 hours a day for days (stoked and simmering at night with some semi-green black oak...coals in the morning).
Here are the specifics of building a system:
Both cookstoves had a serpentine series of pipes in the firebox, mounted vertically on the outboard side (away from the "oven side") and ran from the front of the box to the back in length, inlet and outlet outside at the back. The "coil" was 3/4" galvanized pipe (the "coolness" of the water keeps the galvanizing from melting). Both employed threaded "U" bends that used to be common for this purpose allowing about 3/4" -1" between the pipes. The serpentine used three "U"s, four pipes front to back. Cold water enters the pipes the lower pipe and heated water exits the top pipe. This is the extent of the heating side.
The storage system is a 30gal water tank. It is mounted as close to the firebox as possible, usually next to the stove. Two installations had the tank in the kitchen on the oven side of the stove and two installations had tanks in adjacent rooms, once a bedroom and once a bathroom. We always used an uninsulated tank for two reasons. First, by running your hand down the tank you could tell how hot the water was and how much hot water was available. Second, we valued the tank "heat-loss" as an asset, providing a heat sink to release the stored energy into the room during the night.
The tank is plumbed with two inlets and two outlets. Two connect to the firebox loop and the other two connect to the domestic hot and cold water piping.
Plumbing the heat side follows the laws of thermo-siphon. The heat "loop" exits the tank via a side tap about 1/4 from the bottom, connects to the serpentine piping in the firebox, and re-enters the tank in the upper 1/4. Elevate your tank so that the tank outlet to the firebox is level, or a tad lower, than the lower pipe in the firebox. Keep your low tank-firebox- high tank plumbing at least level, or better, running "uphill" from cool tank outlet to hot tank inlet. The thermo-siphon circulation depends on this principle
On the domestic side, cold incoming water is supplied to an inlet in the lower 1/8 - 1/4 of the tank. This can be a side-tank inlet or run down an internal pipe through the tank top like a conventional gas water heater. Heated water for domestic use exits the tank through the top of the tank and connects in conventional manner to your house hot water piping.
I don't know if anyone still makes the "U" bends for the firebox loop. Maybe research boiler or heat exchanger parts. You may need to use a 90 degree street bend and a regular 90 elbow but your spacing won't be as close thus less pipe length for a given vertical firebox height. In a pinch, maybe two black iron or stainless regular 90 degree elbows could be welded. I vaguely recall a friend may have had a copper pipe system and I know copper "U"s are still available. I'd check first on the melting point of silver solder but since the temp relief valve never opened I'd guess a copper/silver solder loop would work as long as the loop was never run dry.
We always used a galvanized storage tank, also made for this use, with the correct inlet/outlet configurations. Perhaps a discarded electric hot water tank could be used if you could find threaded flange fittings to replace the upper/lower electric heating elements. Hydraulic shops have these but they won't be galvanized.
BTW - For those that may have noticed my absence the past few months I got hammered with 50 - 65 hr work weeks on the "other side" of my semi-retirement. I did get the chance to build a root tooth and a trenching "banana" bucket for the BX and a bit of seat time as well as reading some posts from time to time. Hi to all.
Ray