# Woodstove Energy Production and Efficiency

## Energy Production from a Radiant Woodstove

Most woodstoves on the market and in people's homes are radiant woodstoves, that is, not having any blowers as part of them. For these stoves, there is a rather simple way to calculate the actual heat output being given to a room at any moment.

For all situations where heat is ONLY radiated away, there is a standard equation that describes this so-called Black Body Radiation. The Stefan-Boltzmann Law is that the amount of radiation is equal to a constant (called the Stefan-Boltzmann constant!) times the area of surface times the FOURTH power of the absolute temperature. For a situation where a radiating object is within a room which is at a lower temperature, it becomes = σ * A * (T14 - T24). (We are leaving out here the constants regarding the emissivities of the surfaces involved, assuming them both to be 1.0). A is the total surface area that is radiating, and T1 is the AVERAGE temperature of that surface and T2 is the temperature of the room walls. Temperatures are in R, from absolute zero of -459°F. (The emissivity values have to do with how "black" the surfaces are regarding radiation.)

If all of a woodstove's area were at 800°F (which is 1259°R) and the room was at 70°F (which is 529°R) and the radiating area were 10 square feet, this could be easy! A = 10, σ is 0.1713 * 10-8 Btu/sf/hr/°R4, T1 = 1259°R, and T2 = 529°R. Therefore, we have a total amount of radiation as being:

200°F1,889 Btu/hr
250°F2,987 Btu/hr
300°F4,343 Btu/hr
350°F5,996 Btu/hr
400°F7,985 Btu/hr
450°F10,354 Btu/hr
500°F13,147 Btu/hr
550°F16,413 Btu/hr
600°F20,203 Btu/hr
650°F24,569 Btu/hr
700°F29,568 Btu/hr
750°F35,257 Btu/hr
800°F41,697 Btu/hr

It turns out that most owners tend to operate radiant woodstoves at around 500°F, where it provides around 13,000 Btu/hr for the room. This is a suitable amount of heat for a good sized room without overheating it. However, manufacturers tend to advertise their products with the highest possible claims, and 800°F being fairly obvious dark red glow, few choose to claim higher than around 40,000 Btu/hr maximum. (Blood red glow is around 1000°F, where a lot of owners tend to get scared!)

There is another reason why most owners tend to fire their radiant stoves at around 13,000 Btu/hr. Few modern woodstoves have fireboxes big enough for more than maybe 20 pounds of wood. At 6,000 Btu/pound of good hardwood, this is around 120,000 total Btus of chemical energy available. If a product achieves 60% efficiency (which can be done but rarely is in actual use), we have a total of around 72,000 Btu of energy in the wood available. If used up at 40,000 Btu/hr, all that wood would be burned up in under two hours. At 13,000 Btu/hr, between five and six hours of burn are achieved. Most woodstove owners consider that a tolerable burn time (except during the night!) If that same stove was held back to only supply 9,000 Btu/hr, it could go around eight hours before needing more wood.

This is the briefest possible description of the Physics behind the operation of any radiant woodstove!

This presentation was first placed on the Internet in May 2007.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago