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Buried Pipeline and Frost Bulb Growth

Buried Pipeline and Frost Bulb Growth

Buried Pipeline and Frost Bulb Growth

(OP)
I am working on a specific project in which I need to somehow calculate the frost bulb growth surrounding a buried pipeline. The pipeline is around -4C (Joule Thompson effect) while the surrounding soild is around 5C. The pipe is NPS 8 and uninsulated.

The question is, can anyone offer any direction in calculating the size of the frost growth surrounding the pipeline as a function of time? I am really looking for a model to use, some sort of simplifying assumptions that can be suggested, important information that I must consider... anything really. Anything I have tried to date, basically calculations from first principles of heat xfer and thermo, has ended up being too complex.

If you have come across such a calculation and can offer any advice, I would be greatly appreciated.

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