3. Modeling A

3.1. Characteristics of modeling

AXIS - FOURIER (TRIA6)

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

Fashion - Fourier: 1 \(T(A)=0.\)

\(S=-3.\)	all over the domain
\([\mathrm{BC}]\):	\(\phi =2.\)
\([\mathrm{CD}]\):	\(h=2.\) \({T}_{\mathrm{ext}}=2.\)

3.2. Characteristics of the mesh

Number of knots: 25

Number of meshes and types: 8 TRIA6

3.3. notes

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

Using the CREA_CHAMP/ASSE command is not a Fourier recombination but a simple validation of this keyword.

3.4. Tested values

	Identification	Reference
\(\theta =0\)	\(T(B)\)
	\(T(F)\)	0.25
	\({\phi }_{r}(B)\)	—2
	\({\phi }_{r}(F)\)	—1.
	\({\phi }_{\theta }(B)\)
	\({\phi }_{\theta }(F)\)	0.5
	\({\phi }_{z}(B)\)
	\({\phi }_{z}(F)\)
\(\theta =45\)	\(T(B)\)	0.7071
	\(T(F)\)	0.177
	\({\phi }_{r}(B)\)	—1.414
	\({\phi }_{r}(F)\)	—0.7071
	\({\phi }_{\theta }(B)\)	—0.707
	\({\phi }_{\theta }(F)\)	—0.3535
	\({\phi }_{z}(B)\)
	\({\phi }_{z}(F)\)
\(\theta =135\)	\(T(B)\)	—0.707
	\(T(F)\)	—0.177
	\({\phi }_{r}(B)\)	1.414
	\({\phi }_{r}(F)\)	0.707
	\({\phi }_{\theta }(B)\)	—0.707
	\({\phi }_{\theta }(F)\)	—0.3535
	\({\phi }_{z}(B)\)
	\({\phi }_{z}(F)\)

3.5. notes

The flow values at the nodes are averaged over the elements containing this node.

It is noted that the exact solution has not been found. This is due to the fact that the numerical integration of the thermal stiffness matrix is approximated (3-point formula of GAUSS). If we used a 6-point formula, we would find the solution exactly.