Code_Aster ®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection


Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND Clé
:
V4.04.102-B Page:
1/6

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

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.102

TPLV102 - Transport of heat by convection
in a parallelepiped

Summary:

This functionality was developed in the code in order to be able to test the nonsymmetrical matrices.

Stationary thermal calculation is carried out on elements of the quadrangle type to 4 nodes.

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

Code_Aster ®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection


Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND Clé
:
V4.04.102-B Page:
2/6

1
Problem of reference

1.1 Geometry



One considers the plane thermal problem of a square cavity (on side equal to 1) where heat
propagate:

· by convection (i.e the particles constituting the medium of the cavity move at a speed
U supposed here constant); speed U is supposed to form an angle of 67.5° with axis X,
· by conduction.

1.2
Material properties

One takes CP = 1
10 6
= -


from where a diffusivity = = -
10 6
CP

U. L
and as one takes U =
one has the Peclet number p =
= +
1
10 6
,
E

(L is the length
characteristic, here L = 1.).

1.3
Boundary conditions and loadings

On segments AB and BC, one imposes a temperature T = 1.

On segment AE, one imposes a temperature T = 0.

On the 2 other sides, one in the condition by defect, namely, one is with null flow.

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

Code_Aster ®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection


Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND Clé
:
V4.04.102-B Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

The reference solution is that recommended by Hughes and Brooks in their article referred to
bibliographical [bib1].

One can take as exact solution the field of temperature of the border projected upstream on
the border downstream according to the direction speed.



2.2
Results of reference

One tests the temperatures on the border between points E and D.



2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
T.J.R. HUGHES, A. BROOKS “A multidimensional design with No crosswind diffusion” -
T.J.R. HUGHES ED., Finite Element Methods for convection doninated flows, AMD Vol. 34
(ASME, New York (1979)).

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

Code_Aster ®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection


Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND Clé
:
V4.04.102-B Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling



Modeling is plane: the grid consists of 100 square elements QUAD4 of equal sizes,
and 50 elements SEG2 on the borders.

· the temperature of 0.0 is imposed on the GROUP_NO d2,
· the temperature equal to 1.0 is imposed on the GROUP_NO C1 and C4.

3.2
Characteristics of the grid

50 SEG2, 100 QUA4

3.3 Functionalities
tested

Commands


AFFE_MODELE AFFE
MODELING “PLAN”
AFFE_CHAM_NO
GRANDEUR
“DEPL_R”
AFFE_CHAR_THER CONVECTION SPEED
(AFFE_CHAM_NO)
MACRO_MATR_ASS MATR_ASS
OPTION
“RIGI_THER_CONV_D'
CALC_VECT_ELEM
OPTION
“CHAR_THER”

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

Code_Aster ®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection


Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND Clé
:
V4.04.102-B Page:
5/6

4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster %
difference
T (N31) x=1.0
1.
1.0009
0.0009
T (N29) x=0.8
1.
0.9920
0.008
T (N27) x=0.6
1. 1.0495 0.0495
T (N25) x=0.4
1. 0.845 0.155
T (N23) x=0.2
0. 0.055 0.155
T (N1) x=0.
0. 0.
0.155

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

Code_Aster ®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection


Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND Clé
:
V4.04.102-B Page:
6/6

5
Summary of the results

Good nonsymmetrical matrix installation of for a plane thermal problem.

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

Outline document