How can I compute heat retention of a heated ceramic floor?

Question

The U.S. department of energy suggests electric radiant floor heat can be cost effective if the floor is preheated during off peak electricity hours if installed within an appropriately massive material such as concrete.

Is there a way I can predict the heat loss of the floor over the course of a winter day? In particular, I'm interested in installing it under ceramic tile installed on an uninsulated wooden subfloor with a basement underneath (i.e. air.)

The article states:

Because of the relatively high cost of electricity, electric radiant floors are usually only cost-effective if they include a significant thermal mass such as a thick concrete floor and your electric utility company offers time-of-use rates.

Time-of-use rates allow you to "charge" the concrete floor with heat during off-peak hours (approximately 9 p.m. to 6 a.m.). If the floor's thermal mass is large enough, the heat stored in it will keep the house comfortable for eight to ten hours without any further electrical input, particularly when daytime temperatures are significantly warmer than nighttime temperatures. This saves a considerable number of energy dollars compared to heating at peak electric rates during the day.

Answer 1

The concept of the storage heater is very common in Britain: they usually include a phase change medium which means that a relatively small mass of material can contain a lot of heat without becoming very hot (the latent heat of fusion provides a "thermal cushion" where the medium can give off a lot of heat at a constant temperature, keeping the rate of heating constant).

But if you are stuck with concrete, you can just compute the heat capacity of the floor: multiply it by the maximum acceptable temperature, and you have your answer. As an example, taking a 5 x 8 meter room with a 20 cm thick concrete floor, you are talking about 5x8x0.2=8 cubic meters of concrete. With a typical density of 2400 kg/m^3 and heat capacity of 0.9 J/g/C, you can store about 8x2400x0.9=1.7E7 J/C. This means that a 4 kW heater could run for 1.7E7/4000=4320 seconds to heat the floor by 1 degree - a 12 hour overnight stint will get you up by 12x3600/4320=10 degrees Celsius.

So yes - you can store a reasonable amount of heat in a concrete floor over night. The numbers you need obviously depend on the dimensions of your room, but I hope the above gets you oriented.

If you put the heating element external to the floor, and use water as a medium to do the actual heating, then at some point in the future you could use other sources of heat (geothermal, solar) to heat the same water and get all the benefits of the warm flooring at a lower cost - and without having to rip out the old infrastructure. Worth considering.