Radial vs circumferential thermal stress

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Hi there

I was wondering if someone could give me some insight on the following question.

Suppose you have a radially asymmetric heat flux in the outer surface of a pipe. The inner surface is cooled. This will give you two temperature gradients; one across the pipe thickness and one along the circumference. Assume you adjust parameters so that both gradients are the same. Which stresses will dominate, those due to the radial gradient (across thickness) or those due to the circumferential gradient (from front to back of the tube).

I want to say that the formers will dominate but don't quite find a physical explanation for it.

Any ideas?

Thanks
 

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