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roldy
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Homework Statement
I have a copper tube with outer radius r2 and inner radius of r1. Half the tube is exposed to the surrounding air while the other half is embedded into the ground. The outside air temperature is T2 and the ground temperature is T3. What is the air temperature inside the tube , T1, after equilibrium is reached. This is not a homework assignment but more of a thought experiment.
Homework Equations
$$\dot{Q} \frac {T_1 - T_2}{R_{Total}}$$
$$\Delta T_{tube} = \dot{Q}R_{pipe}$$
3. The Attempt at a Solution [/B]
I was following along using the method described here https://www.engineersedge.com/heat_transfer/heat_loss_insulated_pipe_13865.htm. I then realized that the resistance of the ground needs to come into play. I'm not sure how to account for this since the problem is no longer symmetric about the axis. One possible way to solve this is to split the tube in half and solve for the temperature change in the top half and the temperature change in the bottom half. Then do another heat transfer analysis for the mixing of the two air "regions" to find the equilibrium temperature. Is this thinking correct? I can't recall from college heat transfer courses if I had such an example as this.
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