Tank Heater vs.Recirculating Hot Water

SteveAE wrote:
West,

You might be right that 5 gallons is overkill. I chose it for two reasons:
1 - it is the size of my hot water tank
2 - given my assumed delta T, it just happens to work out to ~1KW.

Here is the math I used, corrections or suggestions are appreciated:
Given/assume:
- Freshwater tank water temp of 40 degrees
- Water heater hot water temp of 120 degrees
Assuming no line losses or cooling due to replacement water into the water heater, this is a delta T of 80 degrees
Since: 1 BTU = 1 degrees (F) change of one pound of water
Then: 80 degrees x 8.34 lbs/gal (weight of water) = 667 BTU/gal
667 BTU/gal x 5 gal = 3336 BTU
Since: 3412 BTU = 1 KW
Then: 5 gallons of 120 degree water cooled down to 40 degrees will release ~0.98 KW worth of equivalent electrical energy.

I know that this is ideal and the losses will add up.

I am also assuming that all incoming water will be cooled down to 40 degrees. Depending on the outside temp and the amount of water in the tank, there will likely either be further cooling OR the tank water will slowly increase in temperature. But, this is perhaps out of my ability to determine given the data I have. So instead, I was just looking for the amount of heat transferred to the tank compared to a typical resistance (electrical) tank heater.

I suppose I could do heat loss calculations on the tank to determine how much energy is really needed, but again, I don't believe there is enough data to even get close (insulation of the tank to outside, heat transfer from the floor of the trailer to the tank, etc.). So I though it would be easier to use a little experimental data (measure the tank water temp) to determine what was happening instead.

The goal is to be able to eliminate furnace heating of the freshwater tank and still protect it from freezing in temps down to about zero (F). Much below that and I am out of there.

Steve

Your math looks solid but establishing Delta T at 80f isn't necessary (unless you want the water in the fresh water tank the same as the water heater). To establish a continual temp of over 32f (perhaps 40f is a better target), you'll need to know the amount of heat loss at ambient adjacent to the tank and supply lines. Your experimental method of temp measuring in tank will probably bring best results. Off hand, if camping at 0f with cabin temps above 65f, with assumed fresh water temp of 40f, assumed tank placement and lack of total insulation, circulating hot water into the system a couple of times during the night should get it done.