7. E modeling

7.1. Characteristics of modeling

AXIS_FOURIER (TRIA3)

The mesh description axes are \(x(r)\) and \(y(z)\).

Fashion - Fourier: 2 \(T(A)=0.\)

\(S=0.\)	all over the domain
\([\mathrm{BC}]\):	\(\phi =2.\)
\([\mathrm{CD}]\):	\(h=2.\) \({T}_{\mathrm{ext}}=2.\)

7.2. Characteristics of the mesh

Number of knots: 153

Number of meshes and types: 200 TRIA3

7.3. notes

Since the Fourier mode number does not affect the load, the MODE_FOURIER keyword is not required in the CALC_VECT_ELEM command.

7.4. Tested values

Identification	Reference
\(T(B)\)
\(T(C)\)
\(T(D)\)
\(T(F)\)	0.25
\(T(G)\)	0.25
\({\phi }_{r}(B)\)	—2.
\({\phi }_{r}(C)\)	—2.
\({\phi }_{r}(D)\)	—2.
\({\phi }_{r}(F)\)	—1.
\({\phi }_{r}(G)\)	—1.
\({\phi }_{\theta }(B)\)
\({\phi }_{\theta }(C)\)
\({\phi }_{\theta }(D)\)
\({\phi }_{\theta }(F)\)
\({\phi }_{\theta }(G)\)
\({\phi }_{z}(B)\)
\({\phi }_{z}(C)\)
\({\phi }_{z}(D)\)
\({\phi }_{z}(F)\)
\({\phi }_{z}(G)\)

7.5. notes

The poor precision recorded on \({\phi }_{r}(B)\), \({\phi }_{r}(C)\), \({\phi }_{r}(D)\) is explained by the fact that \(B\), \(C\), and \(D\) are edge nodes, so the flows are not averaged over adjacent elements in the direction of the temperature gradient (r direction).

This phenomenon is not found on \({\phi }_{\theta }\), because \({\phi }_{\theta }\) is weighted by \(1/r\).