Extrusion/projection operation for non-local couplings

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Hello, I was wondering what is the right way of using 1D extrusion/projection to a 3D surface. I understand projection decreases the number of dimensions.

What I am trying to do is to project temperature from a 1D pipe to a 3D surface, where x and y will be the pipe wall temperature as a function of z.

Since, the pipe is in non-isothermal conditions, I dont want to average my values. I tried linearizing it to 1D line on my surface, it didnt work.



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