1. Reference problem#

1.1. Geometry#

Each square is meshed with a distinct element type.

_images/10003FD6000019F2000019657F7021F55C4ED73B.svg _images/10009C0800001D5200001B386CEE347C10C3FE20.svg

For all 2D modellings. For 3D modellings. (Note: in AXISet AXIS_DIAG, the axis of rotation is OY and the x-axis therefore corresponds to the radius).

(Note: in 3D_ DIAG, only the 4 hexahedra at the bottom left are meshed).

1.2. Material properties#

The thermal properties applied to the model are:

  • \(\lambda \mathrm{=}1.0W\mathrm{/}m°C\)

1.3. Boundary conditions and loads#

Not defined.

1.4. Temperature field#

The temperature field is directly assigned to the model from a function. For each modeling, the flow calculation is tested for a linear thermal field and for a quadratic thermal field.

For 2D models PLAN and PLAN_DIAG (models A and B), the two fields successively affected are:

  • \(T(X,Y)\mathrm{=}\mathrm{2.X}+\mathrm{3.Y}\)

  • \(T(X,Y)\mathrm{=}{\mathrm{2.X}}^{2}+{\mathrm{3.Y}}^{2}\)

For 2D models AXIS and AXIS_DIAG (C and D models), the two fields successively affected are:

  • \(T(X,Y,Z)\mathrm{=}\mathrm{2.R}+\mathrm{3.Y}\) (with \(R\mathrm{=}\sqrt{{X}^{2}+{Z}^{2}}\mathrm{=}X\) in the \((\mathit{OXY})\) mesh plane)

  • \(T(X,Y,Z)\mathrm{=}{\mathrm{2.R}}^{2}+{\mathrm{3.Y}}^{2}\)

For 3D and 3D_ DIAG models (E and F models), the two fields successively affected are:

  • \(T(X,Y,Z)\mathrm{=}\mathrm{2.X}+\mathrm{3.Y}+\mathrm{4.Z}\)

  • \(T(X,Y,Z)\mathrm{=}{\mathrm{2.X}}^{2}+{\mathrm{3.Y}}^{2}+{\mathrm{4Z}}^{2}\)