4.3.3 T3: One-dimensional transient heat transfer

Products: ABAQUS/Standard  ABAQUS/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   

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.


ElementT, Coarse MeshT, Fine Mesh
DC1D234.54° C (–5.6%)35.51° C (–3.0%)
DC1D335.88° C (–2.0%)36.09° C (–1.4%)
DC2D334.54° C (–5.6%)35.51° C (–3.0%)
DC2D434.54° C (–5.6%)35.51° C (–3.0%)
DC2D636.27° C (–0.9%)36.14° C (–1.3%)
DC2D835.88° C (–2.0%)36.09° C (–1.4%)
DCAX334.54° C (–5.6%)35.51° C (–3.0%)
DCAX434.54° C (–5.6%)35.51° C (–3.0%)
DCAX635.91° C (–1.9%)36.10° C (–1.4%)
DCAX835.88° C (–2.0%)36.09° C (–1.4%)
DS334.54° C (–5.6%)36.20° C (–1.1%)
DS434.54° C (–5.6%)35.51° C (–3.0%)
DS635.37° C (–3.4%)36.14° C (–1.3%)
DS835.88° C (–2.0%)36.09° C (–1.4%)
CAX4T34.54° C (–5.6%)35.51° C (–3.0%)
CAX4RT34.54° C (–5.6%)35.51° C (–3.0%)
CAX4RHT34.54° C (–5.6%)35.51° C (–3.0%)
CAX6MHT35.37° C (–3.4%)35.85° C (–2.1%)
CAX6MT35.37° C (–3.4%)35.85° C (–2.1%)
CPE4T34.54° C (–5.6%)35.51° C (–3.0%)
CPE4RT34.54° C (–5.6%)35.51° C (–3.0%)
CPE4RHT34.54° C (–5.6%)35.51° C (–3.0%)
CPE6MT35.81° C (–2.2%)36.0° C (–1.6%)
CPE6MHT35.81° C (–2.2%)36.0° C (–1.6%)
CPS4T34.54° C (–5.6%)35.51° C (–3.0%)
CPS4RT34.54° C (–5.6%)35.51° C (–3.0%)
CPS6MT35.81° 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.


ElementT, Coarse MeshT, Fine Mesh
CAX3T34.98° C (–4.4%)36.08° C (–1.4%)
CAX4RT34.99° C (–4.4%)36.10° C (–1.4%)
CPE3T35.08° C (–4.2%)36.16° C (–1.2%)
CPE4RT35.09° C (–4.1%)36.27° C (–0.9%)
CPS3T35.08° C (–4.2%)36.16° C (–1.2%)
CPS4RT35.09° 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.

Fine mesh tests:


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.

ABAQUS/Explicit input files