T3: One-dimensional transient heat transfer | ||
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ProductsAbaqus/StandardAbaqus/Explicit
Elements tested
- DC1D2
- DC1D3
- DC2D3
- DC2D4
- DC2D6
- DC2D8
- DCAX3
- DCAX4
- DCAX6
- DCAX8
- DS3
- DS4
- DS6
- DS8
- CAX3T
- CAX4T
- CAX4RT
- CAX4RHT
- CAX6MT
- CAX6MHT
- CPE3T
- CPE4T
- CPE4RT
- CPE4RHT
- CPE6MT
- CPE6MHT
- CPS3T
- CPS4T
- CPS4RT
- CPS6MT
- S3RT
- S4RT
Problem description
Model:
The geometry is shown above. A uniform mesh with 5 elements along the length of the bar is used. The thickness and width of the bar are each 0.01 m. A transient simulation is performed. The total simulation time is 32 seconds.
Material:
Conductivity = 35.0 W/m°C, specific heat = 440.5 J/kg°C, density = 7200 kg/m3.
For coupled temperature-displacement elements dummy mechanical properties are used to complete the material definition.
Boundary conditions:
Temperature prescribed as 0°C at end A, and as 100 °C at end B, where t is time in seconds. No heat flux perpendicular to AB.
Loading:
Zero internal heat generation.
Initial conditions
All temperatures = 0°C.
Reference solution
This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test T3 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.
Target solution: Temperature of 36.60°C at 0.08 m at 32 secs.
Results and discussion
The results from the Abaqus/Standard analysis are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.
| Element | T, Coarse Mesh | T, Fine Mesh |
|---|---|---|
| DC1D2 | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| DC1D3 | 35.88°C (−2.0%) | 36.09°C (−1.4%) |
| DC2D3 | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| DC2D4 | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| DC2D6 | 36.27°C (−0.9%) | 36.14°C (−1.3%) |
| DC2D8 | 35.88°C (−2.0%) | 36.09°C (−1.4%) |
| DCAX3 | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| DCAX4 | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| DCAX6 | 35.91°C (−1.9%) | 36.10°C (−1.4%) |
| DCAX8 | 35.88°C (−2.0%) | 36.09°C (−1.4%) |
| DS3 | 34.54°C (−5.6%) | 36.20°C (−1.1%) |
| DS4 | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| DS6 | 35.37°C (−3.4%) | 36.14°C (−1.3%) |
| DS8 | 35.88°C (−2.0%) | 36.09°C (−1.4%) |
| CAX3T | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CAX4T | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CAX4RT | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CAX4RHT | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CAX6MHT | 35.37°C (−3.4%) | 35.85°C (−2.1%) |
| CAX6MT | 35.37°C (−3.4%) | 35.85°C (−2.1%) |
| CPE3T | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CPE4T | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CPE4RT | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CPE4RHT | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CPE6MT | 35.81°C (−2.2%) | 36.0°C (−1.6%) |
| CPE6MHT | 35.81°C (−2.2%) | 36.0°C (−1.6%) |
| CPS3T | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CPS4T | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CPS4RT | 34.54°C (−5.6%) | 35.51°C (−3.0%) |
| CPS6MT | 35.81°C (−2.2%) | 36.0°C (−1.6%) |
The results from the Abaqus/Explicit analysis are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.
| Element | T, Coarse Mesh | T, Fine Mesh |
|---|---|---|
| CAX3T | 34.98°C (−4.4%) | 36.08°C (−1.4%) |
| CAX4RT | 34.99°C (−4.4%) | 36.10°C (−1.4%) |
| CPE3T | 35.08°C (−4.2%) | 36.16°C (−1.2%) |
| CPE4RT | 35.09°C (−4.1%) | 36.27°C (−0.9%) |
| CPS3T | 35.08°C (−4.2%) | 36.16°C (−1.2%) |
| CPS4RT | 35.09°C (−4.1%) | 36.27°C (−0.9%) |
| S3RT | 34.98°C (−4.4%) | 36.08°C (−1.4%) |
| S4RT | 35.09°C (−4.1%) | 36.27°C (−0.9%) |
Input files
Abaqus/Standard input files
Coarse mesh tests:- nt3xx12c.inp
-
DC1D2 elements.
- nt3xx13c.inp
-
DC1D3 elements.
- nt3xx23c.inp
-
DC2D3 elements.
- nt3xx24c.inp
-
DC2D4 elements.
- nt3xx26c.inp
-
DC2D6 elements.
- nt3xx28c.inp
-
DC2D8 elements.
- nt3xxa3c.inp
-
DCAX3 elements.
- nt3xxa4c.inp
-
DCAX4 elements.
- nt3xxa6c.inp
-
DCAX6 elements.
- nt3xxa8c.inp
-
DCAX8 elements.
- nt3xxs3c.inp
-
DS3 elements.
- nt3xxs4c.inp
-
DS4 elements.
- nt3xxs6c.inp
-
DS6 elements.
- nt3xxs8c.inp
-
DS8 elements.
- onedtransienthtc_std_cax3t.inp
-
CAX3T elements.
- onedtransienthtc_std_cax4t.inp
-
CAX4T elements.
- onedtransienthtc_std_cax4rt.inp
-
CAX4RT elements.
- onedtransienthtc_std_cax4rht.inp
-
CAX4RHT elements.
- onedtransienthtc_std_cax6mht.inp
-
CAX6MHT elements.
- onedtransienthtc_std_cax6mt.inp
-
CAX6MT elements
- onedtransienthtc_std_cpe3t.inp
-
CPE3T elements.
- onedtransienthtc_std_cpe4t.inp
-
CPE4T elements.
- onedtransienthtc_std_cpe4rt.inp
-
CPE4RT elements.
- onedtransienthtc_std_cpe4rht.inp
-
CPE4RHT elements.
- onedtransienthtc_std_cpe6mt.inp
-
CPE6MT elements.
- onedtransienthtc_std_cpe6mht.inp
-
CPE6MHT elements.
- onedtransienthtc_std_cps3t.inp
-
CPS3T elements.
- onedtransienthtc_std_cps4t.inp
-
CPS4T elements.
- onedtransienthtc_std_cps4rt.inp
-
CPS4RT elements.
- onedtransienthtc_std_cps6mt.inp
-
CPS6MT elements.
- nt3xx12f.inp
-
DC1D2 elements.
- nt3xx13f.inp
-
DC1D3 elements.
- nt3xx23f.inp
-
DC2D3 elements.
- nt3xx24f.inp
-
DC2D4 elements.
- nt3xx26f.inp
-
DC2D6 elements.
- nt3xx28f.inp
-
DC2D8 elements.
- nt3xxa3f.inp
-
DCAX3 elements.
- nt3xxa4f.inp
-
DCAX4 elements.
- nt3xxa6f.inp
-
DCAX6 elements.
- nt3xxa8f.inp
-
DCAX8 elements.
- nt3xxs3f.inp
-
DS3 elements.
- nt3xxs4f.inp
-
DS4 elements.
- nt3xxs6f.inp
-
DS6 elements.
- nt3xxs8f.inp
-
DS8 elements.
- onedtransienthtf_std_cax3t.inp
-
CAX3T elements.
- onedtransienthtf_std_cax4rt.inp
-
CAX4RT elements.
- onedtransienthtf_std_cax4rht.inp
-
CAX4RHT elements.
- onedtransienthtf_std_cax6mht.inp
-
CAX6MHT elements.
- onedtransienthtf_std_cax6mt.inp
-
CAX6MT elements.
- onedtransienthtf_std_cpe3t.inp
-
CPE3T elements.
- onedtransienthtf_std_cpe4t.inp
-
CPE4T elements.
- onedtransienthtf_std_cpe4rt.inp
-
CPE4RT elements.
- onedtransienthtf_std_cpe4rht.inp
-
CPE4RHT elements.
- onedtransienthtf_std_cpe6mt.inp
-
CPE6MT elements.
- onedtransienthtf_std_cpe6mht.inp
-
CPE6MHT elements.
- onedtransienthtf_std_cps3t.inp
-
CPS3T elements.
- onedtransienthtf_std_cps4t.inp
-
CPS4T elements.
- onedtransienthtf_std_cps4rt.inp
-
CPS4RT elements.
- onedtransienthtf_std_cps6mt.inp
-
CPS6MT elements.
Abaqus/Explicit input files
Coarse mesh tests:- onedtransienthtc_xpl_cax3t.inp
-
CAX3T elements.
- onedtransienthtc_xpl_cax4rt.inp
-
CAX4RT elements.
- onedtransienthtc_xpl_cpe3t.inp
-
CPE3T elements.
- onedtransienthtc_xpl_cpe4rt.inp
-
CPE4RT elements.
- onedtransienthtc_xpl_cps3t.inp
-
CPS3T elements.
- onedtransienthtc_xpl_cps4rt.inp
-
CPS4RT elements.
- onedtransienthtc_xpl_s4rt.inp
-
S4RT elements.
- onedtransienthtf_xpl_cax3t.inp
-
CAX3T elements.
- onedtransienthtf_xpl_cax4rt.inp
-
CAX4RT elements.
- onedtransienthtf_xpl_cpe3t.inp
-
CPE3T elements.
- onedtransienthtf_xpl_cpe4rt.inp
-
CPE4RT elements.
- onedtransienthtf_xpl_cps3t.inp
-
CPS3T elements.
- onedtransienthtf_xpl_cps4rt.inp
-
CPS4RT elements.
- onedtransienthtf_xpl_s3rt.inp
-
S3RT elements.