1. Reference problem#
1.1. Geometry#
We are dealing with a one-dimensional problem in Cartesian coordinates. The « structure » considered is finally a segment of length 1

1.2. Boundary conditions and loads#
A pressure varying linearly from \(P\) in \(x\mathrm{=}0\) to \(0\) in \(x\mathrm{=}1\) is imposed:
In \(x\mathrm{=}0\): the temperature is imposed zero
In \(x\mathrm{=}1\): the temperature is set to 1.
1.3. Initial conditions#
\(T(x)\mathrm{=}0\) everywhere
We are interested in the permanent regime