Thanks Kyle for helping me finish the question of how fast!
1.5" x 42" x 37" = 2331 in^3
about 10.01gal or .0381m^3
Volumetric heat capacity of water:
How much energy
to raise the tank's water from 42F/5.56C to 140F/60C?
410 watts/m^2 from sun but with losses say 328 watts/m^2 from the sun
How fast (which I tried using the Thermal Conductivity to answer
rather than the applied energy).
Why did I choose that route? Because doing so would simultaneously tell me how fast my water would cool down (in a symetrical world).
Finally I gave in to both engineers and used the applied heat; the answer
was easily found of course
9.97Megajoules/(328J/s) = 8h 27 min
well, that aint happening.
sumin gotta change cause I want that water to do 54.4C delta T in 2 hours
I am thinking of that little SAH heating a very small volume quickly and the large room volume inna 1 hour forty.....now how to do that with water and still live :]