Hot *AIR* compost heater biomeiler

Help? We have a question for the engineers/physics gurus out there with a good understanding of heat transfer into air:

My partner and I are building a Jean Pain style compost heater (biomeiler). It's going to be enormous (about 20' diameter circle, 6' tall) and mostly carbon materials for slow heat (70% C, and about 30% N). We're experienced composters, and we live in the humid, rainy mountains of Virginia. There's no difficulty getting compost piles here to very high temperatures for a good long period, so that's the easy part for us. We know from experience that it will get hot enough (over 120°F) for at least 3 months, which is plenty for our needs.

The difficulty is calculating how much air ducting we need (we're planning on using non-perforated drain tile or spiral tubing of some variety, about 4" diameter). We want to run the air into the window of our house directly, which is why it's important that the tubing be fully sealed. The intake can either come from our basement or just the outside air (secured by hardware cloth against pests). Winter air temperatures here rarely drop below 20°F, and never for more than a week or two in a year.

We can't find much discussion online of heating AIR this way, even though there are plenty of mentions of people using it successfully. Most information focuses on using water, or a working fluid heat exchanger. We specifically do not want to do that style; we want to heat air directly and feed it straight into the house. It's only to supplement our woodstove, and smooth out the rollercoaster of hot/cold cycles between times when we're running the woodstove.

So we have two main questions:

1) how do we calculate thermosiphoning in an air system? We'd like to calculate that for small passive solar air heaters as well. Yes, we'll probably end up using a fan to move air through the heater, but it would be nice to understand the math involved in thermosiphoning for air first.

2) how do we calculate the rate of heat exchange from the compost pile/heater into air, through plastic ducts/tubing? If we have no air flow, we know the air in the tubing will heat up, but if we have a blower forcing the air to move through it, how fast should it be blowing, or how long should it run in intermittent cycles? Or, if it blows at a constant rate of airflow, how do we calculate the heat harvest per linear foot of tubing running through the heater?

Example:
If the interior of the pile remains around 140°F, and we have 80' of 4" drain tubing coiled in a vertical spiral through the layers of the pile, and we use a computer fan to move the air at 50 cubic feet per minute, and the air temperature is 25°F at the intake, what will the outflow air temperature be?

Any help with understanding the calculations, or suggestions for which equations we should use, would be very welcome! Thanks in advance!

I think trying to math out the final temp would be too difficult because your outdoor temp and humidity will regularly change your input. What I would try is if it's a PC case fan: those fans can handle a range of voltages so you could adjust the fan voltage to adjust the air flow. Then you can sit a thermometer in the path of the air flow as it enters the window, and see what temps you get at different voltages. Like I've seen case fan switches that have low/med/high as options, so you could possibly adjust it that way too.

I wanted to do similar calculations before building a thermosiphoning passive solar system... but I gave up! Too many variables and unknowns. The ambient air temp/solar gain always changing, unknown values on heat transfer and air resistance in your ducting, that sort of thing.

Measuring what is does produce might be possible after the fact, but predicting ahead of time very well might not be. I figure I'll get return on investment eventually, even though my analytical side wants more specifics.

Maybe you could find something out empirically. Get your tubing, fan, and an IR thermometer. Coil the tubing just like you would in the pile and first see if your fan moves enough air. Pull warm air from inside your house and exhaust it it outdoors on a cold day, Measure both indoor and outdoor temps, and the exhaust temperature, even a few places along the tube?  Try this at different speeds, if that is an option. I would imagine that faster/more air would have a higher exhaust temperature, and slower/less air would have a cooler exhaust. It would be good to do this with a bigger deltaT, between in/out temps. maybe a cold morning at dawn? It won't be a 70* swing, like 70* indoors/ 140* in biomeiler, but would be easier to discern how it works than if it was only say a 10* swing.

In practice, you might want a thermostat to control the fan based on whether the exhaust into the house is still warm enough. This would allow the pile to recharge if the fan was pulling too much heat out.

Try this;

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