Paraffin regression rate in nitrous oxide hybrid fuel grain

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sadben
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i'm trying to model the combustion of a pressurized gas (nitrous oxide) inside of a paraffin ring. What I'm trying to figure out is the amount of paraffin that will be burning per unit time. What I'm assuming is that the gas is totally covering the inside of the wax ring and Ideal Gas law. I'm also assuming that the paraffin does not melt, but burns consistently around the ring. The best way to imagine it is as if the Nitrous is a disk inside a paraffin disc. Also Consider that the Nitrous does not replenish. I'm trying to model hybrid fuel grain regression. I intend to make the model more complicated over time as my research advances and the model evolves.
 
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Well just calculating burn rate in a pressurised environment would be fine. I can figure the rest out