Code_Aster ®
Version
6.4
Titrate:
TPLV101 - Stationary Thermique with exchange between walls
Date:
03/06/03
Author (S):
Key J.P. LEFEBVRE
:
V4.04.101-B Page:
1/8

Organization (S): EDF-R & D/AMA

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.101

TPLV101 - Stationary Thermique with condition
of exchange between walls in opposite

Summary:

This elementary test makes it possible to deal with stationary problem in thermics bringing into play two fields
separated by imposing a boundary condition of the type exchanges between walls.

For modelings presented here, the results obtained by Code_Aster are identical to the reference
calculated analytically.

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
TPLV101 - Stationary Thermique with exchange between walls
Date:
03/06/03
Author (S):
Key J.P. LEFEBVRE
:
V4.04.101-B Page:
2/8

1
Problem of reference

1.1 Geometry

H
G
H
1
1
2
G2
D
D
1
C1
2
C2
L
J1
J2
I
I
1
2
Z
y
F1
F
E
2
1
E2
X
A1
B
With
1
2
B2
L
L
Height L = 3. m
Width I = 1. m


1.2
Material properties

Voluminal heat CP = 0.
Thermal conductivity K = 1.W/m°C

1.3
Boundary conditions and loadings

Outgoing flow through plan B1F1G1C1 identical to flow

entering through plan A 2e2H2 D2
Temperature imposed in A1
T = 0.°C
Temperature imposed in B2
T = 4.5°C
Normal flow imposed on plan B2F2G2C2
= 3.W/m2
Normal flow imposed on plans C1G1H1D1 and C2G2H2 D2
= 6.W/m2
Normal flow imposed on plans E1F1G1H1 and E2F2G2H2
= 2.W/m2
Source imposed in field 1
S
1
Source imposed in field 2
s2

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
TPLV101 - Stationary Thermique with exchange between walls
Date:
03/06/03
Author (S):
Key J.P. LEFEBVRE
:
V4.04.101-B Page:
3/8

2
Reference solution

2.1
Method of calculation used for the reference solution

One has a simple analytical solution, since it is about exhiber a harmonic function and
to adjust the source associated in each field:

· in field 1: T (X, y, Z) = T (1
With)
2
2
2
+ X + y + Z, (in the reference mark of A1 origin),
1
· in field 2: T (X, y, Z) = T (2
With)
2
2
2
+ X + y + Z, (in the reference mark of origin A
2
2).

One deduces the values from them from s1 and s2, s1 = ­ 6. , s2 = ­ 5.W/m3.

2.2
Results of reference

Temperatures at the points of plans B1F1G1C1 and A 2e2H2 D2

2.3
Uncertainty on the solution

Analytical solution.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
TPLV101 - Stationary Thermique with exchange between walls
Date:
03/06/03
Author (S):
Key J.P. LEFEBVRE
:
V4.04.101-B Page:
4/8

3 Modeling
With

3.1
Characteristics of modeling

Modeling 2D:

D1
C
D
1
2
C2
N14
N33
N16
N36
N9
N28
N11
N31
N3
N22
N6
N26
N2
N19
With
With
1
B1
2
B

2
3.2
Boundary conditions and loadings

Outgoing flow through wall B1C1 identical to entering flow

through wall A 2d2
Temperature imposed in A1
T = 0.°C
Temperature imposed in B2
T = 4.5°C
Normal flow imposed on wall B2C2
= 3.W/m2
Normal flow imposed on the plans C1D1 and C 2d2
= 6.W/m2
Source imposed in field 1
S
1
Source imposed in field 2
s2

3.3
Characteristics of the grid
6 QUAD8
36 nodes

3.4
Functionalities tested

Order
Key word factor
Simple key word
Argument
DEFI_MATERIAU THER
LAMBDA



CP


AFFE_CHAR_THER SOURCE



TEMP_IMPO



FLUX_REP



ECHANGE_PAROI



LIAISON_GROUP
STATIONARY THER_LINEAIRE TEMP_INIT
“OUI”
INCREMENT



Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
TPLV101 - Stationary Thermique with exchange between walls
Date:
03/06/03
Author (S):
Key J.P. LEFEBVRE
:
V4.04.101-B Page:
5/8

4
Results of modeling A

4.1 Values
tested

Identification
Reference
Aster %
difference
Temperature
node N2 (B1) 1.00
1.00
0.0
N3 node
2.00
2.00
0.0
N6 node
1.25
1.25
0.0
N11 node
3.25
3.25
0.0
N9 node
5.00
5.00
0.0
N16 node
7.25
7.25
0.0
node N14 (C1) 10.00
10.00
0.0
node N19 (A2) 2.00
2.00
0.0
N22 node
3.00
3.00
0.0
N26 node
2.25
2.25
0.0
N31 node
4.25
4.25
0.0
N28 node
6.00
6.00
0.0
N36 node
8.25
8.25
0.0
node N33 (D2) 11.00
11.00
0.0

4.2 Remarks

The functions of form of element QUAD8 being of command 2, it is natural to obtain the solution of
reference which is expressed in the form of a polynomial of command 2.

The command file deposited contains a list of moments and calls the command
THER_LINEAIRE to carry out a transitory calculation which is not of interest, the coefficient of
voluminal heat being taken equal to 0.

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
TPLV101 - Stationary Thermique with exchange between walls
Date:
03/06/03
Author (S):
Key J.P. LEFEBVRE
:
V4.04.101-B Page:
6/8

5 Modeling
B

5.1
Characteristics of modeling

Modeling 3D:

B33
A22
A26
B21
B5
B13
A2
A30
B44
B1
A10
A35
B40
A39
B28
A7
A15
B8
A3
B4


5.2
Characteristics of the grid

6 HEXA20
88 nodes

5.3
Functionalities tested

Order
Key word factor
Simple key word
Argument
DEFI_MATERIAU
THER LAMBDA


CP


AFFE_CHAR_THER SOURCE



TEMP_IMPO



FLUX_REP



AFFE_CHAR_THER_F ECHANGE_PAROI



LIAISON_GROUP
STATIONARY THER_LINEAIRE TEMP_INIT
“OUI”
INCREMENT




Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
TPLV101 - Stationary Thermique with exchange between walls
Date:
03/06/03
Author (S):
Key J.P. LEFEBVRE
:
V4.04.101-B Page:
7/8

6
Results of modeling B

6.1 Values
tested

Identification
Reference
Aster
% difference
Temperature
node A2 (B1) 1.00
1.00
0.0
node A3 (F1) 2.00
2.00
0.0
A7 node
3.00
3.00
0.0
A10 node
1.25
1.25
0.0
A15 node
2.25
2.25
0.0
A22 node
5.00
5.00
0.0
A26 node
3.25
3.25
0.0
A30 node
5.25
5.25
0.0
node A35 (G1) 11.00
11.00
0.0
A39 node
8.25
8.25
0.0
node B1 (A2) 2.00
2.00
0.0
node B4 (E2) 3.00
3.00
0.0
B5 node
3.00
3.00
0.0
B8 node
4.00
4.00
0.0
B13 node
2.25
2.25
0.0
B21 node
6.00
6.00
0.0
B28 node
5.25
5.25
0.0
node B33 (D2) 11.00
11.00
0.0
B40 node
9.25
9.25
0.0
B44 node
11.25
11.25
0.0

6.2 Remarks

The functions of form of element HEXA20 being of command 2, it is natural to obtain the solution of
reference which is expressed in the form of a polynomial of command 2.

The command file deposited contains a list of moments and calls the command
THER_LINEAIRE to carry out a transitory calculation which is not of interest, the coefficient of
voluminal heat being taken equal to 0.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
TPLV101 - Stationary Thermique with exchange between walls
Date:
03/06/03
Author (S):
Key J.P. LEFEBVRE
:
V4.04.101-B Page:
8/8

7
Summaries of the results

Two modelings with elements of command 2 lead in an exact way to the solution
analytical and the establishment of the boundary conditions of the type ECHANGE_PAROI validates.

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A

Outline document