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pollinator
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It is supposed to have a heat sheild, but I couldn't fit it between the barrel and the wall in the design because the barrel is off scale.
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I think you would be better served by using a "bell" to distribute the exhaust gasses.
The strait line duct will extract less heat into fewer square feet of greenhouse soil.
Matt Walker pioneered building long low bench height bells out of 55 gallon steel barrels cut in half lengthwise.
More recently a similar technique was used to heat the core of a huge mound.
If your green house is say 16' x8', I think you could cover the square footage with 8 barrels.
The larger open spaces within these barrel bells  make it easier for exhaust to slow down and stratify,  yielding a greater heat transfer over a wider area.

Maybe consider using an opaque, insulated thermal mass as the northern wall of the structure,and include the firebox , chimney and  fuel storage within the mass.

 
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I talked to Matt about the half barrel system.   He thought that 6 half barrels was about the max for an 8" J tube. You might even need to use a sliding plunger tube to help start the draft.

The barrels are low , you could put a raised heated starter bed on top of them.
 
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