How to create a constant current source from a 12V,19AH Battery which is load independent?
The most straightforward solution is putting a resistor in series of the right value: 12V (nom) / 10 A = 1.2 ohm. Depending on the battery capacity (Ah) and the state of charge, the voltage at its terminals while discharging might be more (fully charged, large battery) or slightly less.
Good. But this is your heater itself! So, all the dissipated heat shall go to your water and in this case your system would be efficiently serving its purpose. Just fabricate a wire arrangement that gives you more or less 1 ohm.
For a conductor Ohm's Law says R = resistivity * length / squaresection = rho*L/S


with copper: hard, because rho when heated to high temperature is still low (something more than 20 mohm/m/mm2; for robustness you may choose a cross section of some mm2, e.g. 4, and you end up with 5 mohm/m, so you need 200 m coil to make 1 ohm. And it's not as hygienic as steel may be
steel: steel has a 20-40 times larger resistivity; wikipedia gives at 20°C temperature 1.7 10^-8 for Copper, 6.9 10^-7 for stainless steel, so 40 times. With this material and same cross section of 4 mm2 you need only 5-6 m of length, that fits your need.
if you have smaller steel wires you can put them in parallel; if you have a total of 2 mm2 cross section, you reduce length to about 3 m.


Of course you might solutions based on DC/DC converters claiming higher efficiency or better regulation. But all the heat you create in the load is going into the water (feeding cables from battery excluded), fine current regulation is not a concern, so the simple scheme calculated above works.
Brown wires are copper feeding cables from battery to heating coil, made of the said steel.







simulate this circuit &ndash; Schematic created using CircuitLab