Thermal surface interaction

Elements tested

DC1D2
DC2D4
DC2D8
DC3D8
DC3D20
DCAX4
DCAX8

DS3
DS4
DS6
DS8
DSAX1
DSAX2

CAX3T
CAX4RT
CPE3T
CPE4RT
CPS3T
CPS4RT

C3D4T
C3D6T
C3D8RT
SC8RT
SC6RT

Features tested

Contact pair

Gap conductance

Gap radiation

Problem description

A solid material is placed near a heat source whose temperature stays constant. Heat transfer across the gap between the solid surface and the heat source can take place via gap conductance or gap radiation (thus, there are two tests for each element type). Using the default convergence tolerances in Abaqus/Standard, the reaction fluxes for radiation problems show slight differences (0.1%) from the analytical results due to the severe nonlinearity of the radiation problem. We initiate unidirectional heat flow by applying a constant temperature that is higher than that of the heat source itself to the solid surface away from the heat source. The steady-state temperature at the surface near the heat source is used to verify the numerical solutions.

In Abaqus/Explicit the steady-state result is obtained by performing a long-term transient simulation. The constant temperature heat source is modeled three different ways: with either deformable elements, isothermal discrete rigid elements, or an isothermal analytical rigid surface. Both kinematic and penalty mechanical contact are considered.

Model:


Element size	1 unit in each direction
Inner radius of axisymmetric solids	10.0

Material:


Conductivity in solid	1.0
Gap conductance	10.0
Radiation constants of surfaces	5 × 10⁻¹⁰
Absolute zero	−460.0

In Abaqus/Explicit dummy mechanical and capacitance properties are specified to complete the material definition.

Results and discussion

The steady-state temperatures agree with the analytical, one-dimensional heat transfer results.

Input files

Abaqus/Standard input files

Gap conductance tests:

eiu1dgccc.inp: DC1D2, DGAP elements.
ei22discc.inp: DC2D4 elements.
ei23discc.inp: DC2D8 elements.
ei23discc_gc.inp: DC2D8 elements with general contact.
ei34discc.inp: DC3D8 elements.
ei38discc.inp: DC3D20 elements.
ei38discc_gc.inp: DC3D20 elements with general contact.
eia2discc.inp: DCAX4 elements.
eia2discc_gc.inp: DCAX4 elements with general contact.
eia3discc.inp: DCAX8 elements.
eia3discc_gc.inp: DCAX8 elements with general contact.
ei33discs.inp: DS3 elements.
ei33discs_gc.inp: DS3 elements with general contact.
ei33discs_interf_gc.inp: DS3 elements with deep overclosure between heat transfer surfaces modeled using general contact.
ei34discs.inp: DS4 elements.
ei34discs_gc.inp: DS4 elements with general contact.
ei34discs_interf_gc.inp: DS4 elements with deep overclosure between heat transfer surfaces modeled using general contact.
ei36discs.inp: DS6 elements.
ei36discs_gc.inp: DS6 elements with general contact.
ei36discs_interf_gc.inp: DS6 elements with deep overclosure between heat transfer surfaces modeled using general contact.
ei38discs.inp: DS8 elements.
ei38discs_gc.inp: DS8 elements with general contact.
ei38discs_interf_gc.inp: DS8 elements with deep overclosure between heat transfer surfaces modeled using general contact.
eia2discs.inp: DSAX1 elements.
eia3discs.inp: DSAX2 elements.

Gap radiation tests:

eiu1dgcrc.inp: DC1D2, DGAP elements.
ei22disrc.inp: DC2D4 elements.
ei23disrc.inp: DC2D8 elements.
ei34disrc.inp: DC3D8 elements.
ei38disrc.inp: DC3D20 elements.
eia2disrc.inp: DCAX4 elements.
eia3disrc.inp: DCAX8 elements.
ei33disrs.inp: DS3 elements.
ei33disrs_gc.inp: DS3 elements with general contact.
ei33disrs_interf_gc.inp: DS3 elements with deep overclosure between heat transfer surfaces modeled using general contact.
ei34disrs.inp: DS4 elements.
ei36disrs.inp: DS6 elements.
ei36disrs_gc.inp: DS6 elements with general contact.
ei36disrs_interf_gc.inp: DS6 elements with deep overclosure between heat transfer surfaces modeled using general contact.
ei38disrs.inp: DS8 elements.
eia2disrs.inp: DSAX1 elements.
eia2disrs_gc.inp: DSAX1 elements with general contact.
eia2disrs_interf_gc.inp: DSAX1 elements with deep overclosure between heat transfer surfaces modeled using general contact.
eia3disrs.inp: DSAX2 elements.
eia3disrs_gc.inp: DSAX2 elements with general contact.
eia3disrs_interf_gc.inp: DSAX2 elements with deep overclosure between heat transfer surfaces modeled using general contact.

Abaqus/Explicit input files

Gap conductance tests, deformable-deformable with kinematic mechanical contact:

gapheattrans_c_x_df_cax3t.inp: Solid and heat source modeled with CAX3T elements.
gapheattrans_c_x_df_cax4rt.inp: Solid and heat source modeled with CAX4RT elements.
gapheattrans_c_x_df_cpe3t.inp: Solid and heat source modeled with CPE3T elements.
gapheattrans_c_x_df_cpe4rt.inp: Solid and heat source modeled with CPE4RT elements.
gapheattrans_c_x_df_cps3t.inp: Solid and heat source modeled with CPS3T elements.
gapheattrans_c_x_df_cps4rt.inp: Solid and heat source modeled with CPS4RT elements.
gapheattrans_c_x_df_c3d4t.inp: Solid and heat source modeled with C3D4T elements.
gapheattrans_c_x_df_c3d6t.inp: Solid and heat source modeled with C3D6T elements.
gapheattrans_c_x_df_c3d8rt.inp: Solid and heat source modeled with C3D8RT elements.
gapheattrans_c_x_df_sc8rt.inp: Solid and heat source modeled with SC8RT elements.

Gap conductance tests, deformable-deformable with penalty mechanical contact:

gapheattrans_c_xp_df_cax4rt.inp: Solid and heat source modeled with CAX4RT elements.
gapheattrans_c_xp_df_cpe4rt.inp: Solid and heat source modeled with CPE4RT elements.
gapheattrans_c_xp_df_c3d8rt.inp: Solid and heat source modeled with C3D8RT elements.
gapheattrans_c_xp_df_sc8rt.inp: Solid and heat source modeled with SC8RT elements.

Gap conductance tests, discrete rigid-deformable with kinematic mechanical contact:

gapheattrans_c_x_dr_cax4rt.inp: Solid modeled with CAX4RT elements; constant temperature heat source modeled with RAX2 elements.
gapheattrans_c_x_dr_cpe3t.inp: Solid modeled with CPE3T elements; constant temperature heat source modeled with R2D2 elements.
gapheattrans_c_x_dr_cps4rt.inp: Solid modeled with CPS4RT elements; constant temperature heat source modeled with R2D2 elements.
gapheattrans_c_x_dr_c3d4t.inp: Solid modeled with C3D4T elements; constant temperature heat source modeled with R3D3 elements.
gapheattrans_c_x_dr_c3d8rt.inp: Solid modeled with C3D8RT elements; constant temperature heat source modeled with R3D4 elements.
gapheattrans_c_x_dr_sc8rt.inp: Solid modeled with SC8RT elements; constant temperature heat source modeled with R3D4 elements.

Gap conductance tests, discrete rigid-deformable with penalty mechanical contact:

gapheattrans_c_xp_dr_cax4rt.inp: Solid modeled with CAX4RT elements; constant temperature heat source modeled with RAX2 elements.
gapheattrans_c_xp_dr_cps4rt.inp: Solid modeled with CPS4RT elements; constant temperature heat source modeled with R2D2 elements.
gapheattrans_c_xp_dr_c3d8rt.inp: Solid modeled with C3D8RT elements; constant temperature heat source modeled with R3D4 elements.
gapheattrans_c_xp_dr_sc8rt.inp: Solid modeled with SC8RT elements; constant temperature heat source modeled with R3D4 elements.

Gap conductance tests, analytical rigid-deformable with kinematic mechanical contact:

gapheattrans_c_x_ar_cax4rt.inp: Solid modeled with CAX4RT elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_c_x_ar_cpe3t.inp: Solid modeled with CPE3T elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_c_x_ar_cps4rt.inp: Solid modeled with CPS4RT elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_c_x_ar_c3d4t.inp: Solid modeled with C3D4T elements; constant temperature heat source modeled with an analytical rigid surface.

Gap conductance tests, analytical rigid-deformable with penalty mechanical contact:

gapheattrans_c_xp_ar_cax4rt.inp: Solid modeled with CAX4RT elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_c_xp_ar_cpe3t.inp: Solid modeled with CPE3T elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_c_xp_ar_c3d4t.inp: Solid modeled with C3D4T elements; constant temperature heat source modeled with an analytical rigid surface.

Gap radiation tests, deformable-deformable with kinematic mechanical contact:

gapheattrans_r_x_df_cax3t.inp: Solid and heat source modeled with CAX3T elements.
gapheattrans_r_x_df_cax4rt.inp: Solid and heat source modeled with CAX4RT elements.
gapheattrans_r_x_df_cpe3t.inp: Solid and heat source modeled with CPE3T elements.
gapheattrans_r_x_df_cpe4rt.inp: Solid and heat source modeled with CPE4RT elements.
gapheattrans_r_x_df_cps3t.inp: Solid and heat source modeled with CPS3T elements.
gapheattrans_r_x_df_cps4rt.inp: Solid and heat source modeled with CPS4RT elements.
gapheattrans_r_x_df_c3d4t.inp: Solid and heat source modeled with C3D4T elements.
gapheattrans_r_x_df_c3d6t.inp: Solid and heat source modeled with C3D6T elements.
gapheattrans_r_x_df_c3d8rt.inp: Solid and heat source modeled with C3D8RT elements.
gapheattrans_r_x_df_sc8rt.inp: Solid and heat source modeled with SC8RT elements.

Gap radiation tests, deformable-deformable with penalty mechanical contact:

gapheattrans_r_xp_df_cax3t.inp: Solid and heat source modeled with CAX3T elements.
gapheattrans_r_xp_df_cpe3t.inp: Solid and heat source modeled with CPE3T elements.
gapheattrans_r_xp_df_c3d4t.inp: Solid and heat source modeled with C3D4T elements.

Gap radiation tests, discrete rigid-deformable with kinematic mechanical contact:

gapheattrans_r_x_dr_cax3t.inp: Solid modeled with CAX3T elements; constant temperature heat source modeled with RAX2 elements.
gapheattrans_r_x_dr_cpe4rt.inp: Solid modeled with CPE4RT elements; constant temperature heat source modeled with R2D2 elements.
gapheattrans_r_x_dr_cps3t.inp: Solid modeled with CPS3T elements; constant temperature heat source modeled with R2D2 elements.
gapheattrans_r_x_dr_c3d6t.inp: Solid modeled with C3D6T elements; constant temperature heat source modeled with R3D4 elements.

Gap radiation tests, discrete rigid-deformable with penalty mechanical contact:

gapheattrans_r_xp_dr_cax3t.inp: Solid modeled with CAX3T elements; constant temperature heat source modeled with RAX2 elements.
gapheattrans_r_xp_dr_cps3t.inp: Solid modeled with CPS3T elements; constant temperature heat source modeled with R2D2 elements.
gapheattrans_r_xp_dr_c3d6t.inp: Solid modeled with C3D6T elements; constant temperature heat source modeled with R3D4 elements.

Gap radiation tests, analytical rigid-deformable with kinematic mechanical contact:

gapheattrans_r_x_ar_cax3t.inp: Solid modeled with CAX3T elements; constant temperature heat source with an analytical rigid surface.
gapheattrans_r_x_ar_cpe4rt.inp: Solid modeled with CPE4RT elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_r_x_ar_cps3t.inp: Solid modeled with CPS3T elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_r_x_ar_c3d6t.inp: Solid modeled with C3D6T elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_r_x_ar_c3d8rt.inp: Solid modeled with C3D8RT elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_r_x_ar_sc6rt.inp: Solid modeled with SC6RT elements; constant temperature heat source modeled with an analytical rigid surface.

Gap radiation tests, analytical rigid-deformable with penalty mechanical contact:

gapheattrans_r_xp_ar_cax3t.inp: Solid modeled with CAX3T elements; constant temperature heat source with an analytical rigid surface.
gapheattrans_r_xp_ar_cpe4rt.inp: Solid modeled with CPE4RT elements; constant temperature heat source modeled with an analytical rigid surface.
gapheattrans_r_xp_ar_c3d8rt.inp: Solid modeled with C3D8RT elements; constant temperature heat source modeled with an analytical rigid surface.