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Temperature Profile in Pipe due to Soil

Temperature Profile in Pipe due to Soil

Temperature Profile in Pipe due to Soil

(OP)
What (or where) are the equations for heat transfer between fluid-pipe-soil?

I have a pipeline simulator and am determining the temperature decline of a gas.  The pipeline is buried 3' under the soil line and the soil line is 100' under water.  As I run the model with decreasing flow rate, I found the temperature drops slowly until about a 40% drop in flow rate.  Then the temperature drops a little more rapidly.  What determines this threshold?

I also assumed no significant outer wrap...

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