Unsteady thermal conductivity of a circular plate with boundary conditions of convection and a given temperature
Verification of the LIRA-FEM software / Unsteady thermal conductivity of a circular plate with boundary conditions of convection and a given temperature / W.H.McAdams, Transmission de la chaleur, Paris, Dunod, 1961.
Type of analysis: unsteady thermal.
Source: W.H.McAdams, Transmission de la chaleur, Paris, Dunod, 1961.
Geometry:
D=0.2'
Material Characteristics:
Thermal conductivity coefficient: λ=48.822 ''/' 'C.
Specific heat capacity: Cp=669 ''/'' 'C.
Specific weight: ρ=7200 ''/'3.
Boundary conditions:
convective heat transfer coefficient he=232,5 ''/'2 ' C,
Ambient temperature: T e = 1000 ' C.
Initial temperature: T0 = 20 ' C.
The calculation method used to obtain the reference solution:
- calculation of coefficients.
- values according to the Herny-Lourier diagram.
CALCULATION RESULTS:
|
Time(') |
The desired value |
Analytical solution |
Calculation results (LIRA-SAPR)) |
Uncertainty,% |
|
|
600 |
Surface temperature |
'1 (0') |
461 |
493 |
6.94 |
|
800 |
'1 (0') |
550 |
577 |
4.91 |
|
|
1000 |
'1 (0') |
637 |
647 |
1.57 |
|
|
1200 |
'1 (0') |
686 |
706 |
2.92 |
|
|
1400 |
'1 (0') |
735 |
756 |
2.86 |
|
|
1600 |
'1 (0') |
774 |
798 |
3.10 |
|
|
1800 |
'1 (0') |
813 |
834 |
2.58 |
|
|
2200 |
'1 (0') |
873 |
888 |
1.72 |
|
|
2600 |
'1 (0') |
910 |
927 |
1.87 |
|
|
3000 |
'1 (0') |
936 |
954 |
1.92 |
|
|
3400 |
'1 (0') |
951 |
973 |
2.31 |
|
|
3800 |
'1 (0') |
970 |
987 |
1.75 |
|
|
600 |
Temperature in the center |
'2 (0') |
314 |
360 |
14.65 |
|
800 |
'2 (0') |
412 |
465 |
12.86 |
|
|
1000 |
'2 (0') |
510 |
553 |
8.43 |
|
|
1200 |
'2 (0') |
588 |
628 |
6.80 |
|
|
1400 |
'2 (0') |
657 |
690 |
5.02 |
|
|
1600 |
'2 (0') |
706 |
742 |
5.10 |
|
|
1800 |
'2 (0') |
755 |
787 |
4.24 |
|
|
2200 |
'2 (0') |
828 |
855 |
3.26 |
|
|
2600 |
'2 (0') |
880 |
903 |
2.61 |
|
|
3000 |
'2 (0') |
917 |
937 |
2.18 |
|
|
3400 |
'2 (0') |
941 |
962 |
2.23 |
|
|
3800 |
|
959 |
979 |
2.09 |
|
'''''''''' ''''''':
|
'''''(') |
''''''' '''''''' |
Calculation results (ANSYS*) |
Calculation results (LIRA-SAPR) |
Uncertainty,% |
|
|
600 |
Surface temperature |
'1 (0') |
472 |
493 |
4.45 |
|
800 |
'1 (0') |
556 |
577 |
3.78 |
|
|
1000 |
'1 (0') |
627 |
647 |
3.19 |
|
|
1200 |
'1 (0') |
686 |
706 |
2.92 |
|
|
1400 |
'1 (0') |
736 |
756 |
2.72 |
|
|
1600 |
'1 (0') |
778 |
798 |
2.57 |
|
|
1800 |
'1 (0') |
814 |
834 |
2.46 |
|
|
2200 |
'1 (0') |
868 |
888 |
2.30 |
|
|
2600 |
'1 (0') |
907 |
927 |
2.21 |
|
|
3000 |
'1 (0') |
934 |
954 |
2.14 |
|
|
3400 |
'1 (0') |
954 |
973 |
1.99 |
|
|
3800 |
'1 (0') |
967 |
987 |
2.07 |
|
|
600 |
''''''''''' ' '''''' |
'2 (0') |
350 |
360 |
2.86 |
|
800 |
'2 (0') |
454 |
465 |
2.42 |
|
|
1000 |
'2 (0') |
541 |
553 |
2.22 |
|
|
1200 |
'2 (0') |
614 |
628 |
2.28 |
|
|
1400 |
'2 (0') |
676 |
690 |
2.07 |
|
|
1600 |
'2 (0') |
727 |
742 |
2.06 |
|
|
1800 |
'2 (0') |
771 |
787 |
2.08 |
|
|
2200 |
'2 (0') |
838 |
855 |
2.03 |
|
|
2600 |
'2 (0') |
886 |
903 |
1.92 |
|
|
3000 |
'2 (0') |
920 |
937 |
1.85 |
|
|
3400 |
'2 (0') |
942 |
962 |
2.12 |
|
|
3800 |
|
960 |
979 |
1.98 |
|
Note:
To build the scheme we used FE1509 - quadrangular heat conduction FEs, FE1508 - triangular heat conduction FEs, 1555 - two-node convective heat transfer FEs.
Number of nodes:251.
Number of elements:523.
*In order to correctly calculate the problem in ANSYS it is necessary in the *. db files to redefine the initial conditions (Initial Condition), which are equal to T0 = 20 ' C.
''' ''''' ''''':
Go to the Solution tab, then select Define Loads, then Apply, then Initial Condition, then
Define and select Ok. In the dialog box set 20 degrees and select TEMP (temperature).
Preview image: Array
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