Determining the total energy released by a compost pile

[AamsterC2]

The heat source for this experiment is a compost pile (1 cubic meter), I know that the inside of the pile will reach approximately 50C for 2 weeks or so. Right now it's winter so the temperature will stay around 0C (average). The thermal conductivity of compost can vary greatly but in this case an average that would apply is 0.3 W/m. I'm guessing here but I believe Fourier's Law could apply and I could use that to solve how much energy is lost over the course of two weeks which would also give me how much energy is produced since the energy is constant. Again simplifying I'll say that the inner half of the sphere is 50C and the outer half acts only as insulation so Q = -kA(dT/dx)
Q=Watts, k=thermal conductivity, A=heat transfer area, dT=temperature difference, dx=thickness of barrier
Q = -0.3 * 3.14 (50 / 0.5)
Q = 94.2 W * 1,209,600 (seconds in 2 weeks)
113,944,320 Watts over the course of 2 weeks

Is that the proper way to solve this type problem?

 

[oz93666]

That last line should read "Joules over the course of 2 weeks" ...

This is a very complex situation ,because we don't know how much microbial action is going on in the cool regions , certainly if the outside was 0C not much composting would happen overall... I don't think theory would give a very accurate answer ... Perhaps the best way would be to create a pile that closely resembled the composition and moisture content of the compost heap , but that you knew had no microbial action going on ... and put a 100w electric heating element in the center and see if the temperature profile was similar after a day... even this would not be perfect ...

But 92W sounds it could be about right