Solar Heating Technical Comments 1

Some people who have some knowledge of science see this as ridiculous! They think that plastic tubing would eliminate any decent performance of such a system. As a result, they then assume that we don't know what we are talking about and that this system does not work! Not true. They think that we would have had to describe aluminum tubing or copper tubing for the material. At the very least, iron or steel pipe!

Such people are theoretically correct, but are unaware of the practical engineering involved!.

Any engineering text, or any good heating text will confirm the following.

All "heat exchange" processes involve at least three major effects: (1) a surface film effect in the first fluid (house air, in this case); (2) the thermal conductivity through the material itself; and (3) a surface film effect in the second fluid/material (in our case, the possibly moist soil surrounding the buried tubes).

The standard engineering formula for this is (slightly simplified):
1/U = 1/hi + thickness/k + 1/ho

U is the desired rate of thermal transfer of the heat exchanger, in Btu/hr/sq.ft. hi is the heat-transfer coefficient for the first (incoming) film. ho is the heat-transfer coefficient for the second (outgoing) film. k is the thermal conductivity of the material of the exchanger.

We have forced air passing through our tubes, so hi is given by the standard engineering formula:
hi = 0.024 * Cp * G0.8 / (Di)0.2

If we blow around 2,000 cfm of air through the nine tubes of our normal configuration, Di = 0.33 ft; Cp = 0.241 Btu/lb/F and G = 11,800 lb/hr/ft2, this calculates to around 13 Btu/hr/sq.ft./F

For the other film coefficient, the condition of the soil, particularly its amount of moisture, tremendously affects the value. If the soil was dead dry sand (the worst possible situation) the coefficient could be on the scale of the incoming film value calculated above. However, all practical (deep) soils have substantial moisture content. That water enables excellent direct contact with the tube surfaces, creating very good heat transfer outward, by both conduction and convection. For most moist soils, ho is at least 100 or so. In a dry desert situation, this factor can be rather low.

As to the middle term, the conductivity of the tube material itself: Standard iron pipe of 1/4" thickness has a conductivity of around 1480 Btu/hr/sq.ft./F. The PVC plastic pipe we are recommending has a much lower value, and would only be around 48 Btu/hr/sq.ft./F for a 1/4" thick wall (Schedule 40). We selected the thin wall drain pipe to enable this to be around 120 Btu/hr/sq.ft./F for our choice of material. As we will see, the difference in this term between 1480 and 120 and 48 is nearly irrelevant, because both of the film coefficients are far lower and they always represent the limiting cases.

Now, let's calculate U. If we used (relatively expensive) iron pipe, we would have:
1/U = 1/13 + 1/1480 + 1/100, which gives U as 11.4 Btu/hr/sq.ft./F.

If we use the (thinwall) PVC tubing we recommend, we would have:
1/U = 1/13 + 1/120 + 1/100, which gives U as 10.5 Btu/hr/sq.ft./F.

Even if we use the (Sch 40) thickwall PVC tubing, we would have:
1/U = 1/13 + 1/48 + 1/100, which still gives U as 9.3 Btu/hr/sq.ft./F.

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Yes, this confirms that the better thermal conductivity of iron pipe really DOES give better overall heat transfer. However, notice how little the difference is! Even though iron has about 30 times the thermal conductivity (k) of PVC, the net effect in our heat exchangers is amazingly minimal! Even if very expensive large diameter copper or aluminum pipe was to be used, the calculated value does not get above 11.5 Btu/hr/sq.ft./F.

THIS is why we recommend the PVC pipe. The actual thermal disadvantage is far less than it might seem that it would be. Considering how very inexpensive PVC sewer pipes are, it makes a lot more sense to just add 5% more length of tubing to make up for this difference. Thinwall PVC is also much lighter and much easier to work with than the extremely heavy lengths of large diameter steel tubing or pipe. Anyone is certainly free to use steel pipe, especially if a huge supply of such pipe is inexpensive and available. But for most people, the thinwall PVC seems to be a nearly perfect choicd.

Keep in mind that these calculations assumed that the soil outside the tubes is moderately moist. If it ever gets extremely dry, then the outer film coefficient can become much worse. In that case, the outer film coefficient becomes the limiting factor rather than the inside film coefficient. The material of the tube itself is never the limiting factor! This fact is why we highly recommend installing the soaker poly water lines a foot above the tubes, so if the soil ever gets really dry, you could quickly wet it down and get everything working fine again.

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