Hey Mickey. Good concept there but I will second what William said about aircrete. You'll need to line the interior with refractory or firebrick to get any longevity from the build.
It occurs to me that a "standard" rocket oven design could be perfect for this.
You could run a pipe from the oven back down to the J rocket, or you could just add holes at the bottom of the oven, near where the riser exhausts.
This would avoid more expensive materials like firebrick.
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