# Radiation and convection — Welcome to LS-DYNA Examples

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The basis for this example is a simple roof structure consisting of a wooden panel, insulation and an aluminium outer layer. The internal temperature on the wood surface is kept constant. The outside ambient temperature is also constant but lower than the inside temperature. Five different roof sections are used to demonstrate different definitions for convection and radiation boundary conditions on the surface of the aluminium layer. A transient thermal calculation is carried out.

## Keywords

```*BOUNDARY_CONVECTION_SET
*CONTROL_SOLUTION
*CONTROL_TERMINATION
*CONTROL_THERMAL_NONLINEAR
*CONTROL_THERMAL_SOLVER
*CONTROL_THERMAL_TIMESTEP
*DATABASE_BINARY_D3PLOT
*DATABASE_TPRINT
*DEFINE_CURVE
*DEFINE_FUNCTION
*ELEMENT_SOLID
*END
*INCLUDE
*INITIAL_TEMPERATURE_SET
*KEYWORD
*MAT_THERMAL_ISOTROPIC
*NODE
*PART
*SECTION_SOLID
*SET_NODE_LIST_TITLE
*SET_SEGMENT_TITLE
*TITLE
```

## Reduced Input

```*KEYWORD
\$
\$=============================CONTROL DEFINITIONS ==============================
\$
*TITLE
transient heat transfer through an insulated aluminium roof
*CONTROL_SOLUTION
\$ thermal only
\$     soln       nlq     isnan     lcint     lcacc     ncdcf
1
*CONTROL_THERMAL_SOLVER
\$ transient thermal analysis
\$    atype     ptype    solver     cgtol       gpt    eqheat     fwork       sbc
1         1        11
\$   msglvl    maxitr    abstol    reltol     omega                           tsf

*CONTROL_THERMAL_TIMESTEP
\$       ts       tip       its      tmin      tmax     dtemp      tscp      lcts
1       1.0        60      30.0    3600.0
*CONTROL_THERMAL_NONLINEAR
\$   refmax       tol       dcp    lumpbc    thlstl    nlthpr    phchpn

*CONTROL_TERMINATION
\$   endtim    endcyc     dtmin    endeng    endmas     nosol
288000.0
\$
\$================================ OUTPUTDATA ===================================
\$
*DATABASE_BINARY_D3PLOT
\$       dt
300.0
*DATABASE_GLSTAT
\$       dt
300.0
*DATABASE_MATSUM
\$       dt
300.0
*DATABASE_TPRINT
\$       dt
60.0
\$
\$============================== PART DEFINITIONS ===============================
\$
*PART
\$ title
wood_panel
\$      pid     secid       mid     eosid      hgid      grav    adpopt      tmid
1         1         0         0         0         0         0         1
*PART
\$ title
insulation
\$      pid     secid       mid     eosid      hgid      grav    adpopt      tmid
2         1         0         0         0         0         0         2
*PART
\$ title
aluminium_sheet
\$      pid     secid       mid     eosid      hgid      grav    adpopt      tmid
3         1         0         0         0         0         0         3
\$
\$============================= SECTION PROPERTIES ==============================
\$
*SECTION_SOLID
\$    secid    elform
1         1
\$
\$======================== THERMAL MATERIAL PROPERTIES ==========================
\$
*MAT_THERMAL_ISOTROPIC
\$ wood_panel
\$     tmid       tro     tgrlc    tgmult      tlat      hlat
1   6.5e-10
\$       hc        tc
1.7e9      0.12
*MAT_THERMAL_ISOTROPIC
\$ insulation
\$     tmid       tro     tgrlc    tgmult      tlat      hlat
2   1.0e-10
\$       hc        tc
9.0e8      0.04
*MAT_THERMAL_ISOTROPIC
\$ aluminium_sheet
\$     tmid       tro     tgrlc    tgmult      tlat      hlat
3    2.7e-9
\$       hc        tc
8.97e8     236.0
\$
\$=======================NODE/ELEMENT/SET/SEGMENT DEFINTIONS ====================
\$
*INCLUDE
02_insulated_aluminium_roof_parts.k
*SET_NODE_LIST_TITLE
inside
\$      sid       da1       da2       da3       da4    solver
1       0.0       0.0       0.0       0.0MECH
\$     nid1      nid2      nid3      nid4      nid5      nid6      nid7      nid8
2        35        34         1         3        36        68        67
...       ...       ...       ...       ...       ...       ...       ...
*SET_SEGMENT_TITLE
outside_boundary_convection
\$      sid       da1       da2       da3       da4    solver
1       0.0       0.0       0.0       0.0MECH
\$       n1        n2        n3        n4        a1        a2        a3        a4
144       166       167       145       0.0       0.0       0.0       0.0
145       167       168       146       0.0       0.0       0.0       0.0
166       188       189       167       0.0       0.0       0.0       0.0
167       189       190       168       0.0       0.0       0.0       0.0
*SET_SEGMENT_TITLE
\$      sid       da1       da2       da3       da4    solver
2       0.0       0.0       0.0       0.0MECH
\$       n1        n2        n3        n4        a1        a2        a3        a4
1044      1050      1051      1045       0.0       0.0       0.0       0.0
...       ...       ...       ...       ...       ...       ...       ...
*SET_SEGMENT_TITLE
\$      sid       da1       da2       da3       da4    solver
3       0.0       0.0       0.0       0.0MECH
\$       n1        n2        n3        n4        a1        a2        a3        a4
1305      1311      1312      1306       0.0       0.0       0.0       0.0
...       ...       ...       ...       ...       ...       ...       ...
*SET_SEGMENT_TITLE
\$      sid       da1       da2       da3       da4    solver
4       0.0       0.0       0.0       0.0MECH
\$       n1        n2        n3        n4        a1        a2        a3        a4
1566      1572      1573      1567       0.0       0.0       0.0       0.0
...       ...       ...       ...       ...       ...       ...       ...
*SET_SEGMENT_TITLE
\$      sid       da1       da2       da3       da4    solver
5       0.0       0.0       0.0       0.0MECH
\$       n1        n2        n3        n4        a1        a2        a3        a4
1827      1833      1834      1828       0.0       0.0       0.0       0.0
...       ...       ...       ...       ...       ...       ...       ...
\$
\$==================== THERMAL BOUNDARY and INITIAL CONDITIONS ==================
\$
*INITIAL_TEMPERATURE_SET
\$  nid/sid      temp       loc
0    293.15
*BOUNDARY_CONVECTION_SET
\$ convection boundary on outerside of the aluminum sheet "column 1"
\$     ssid
1
\$    hlcid     hmult     tlcid     tmult       loc
0      0.01         0    273.15
\$ convection boundary on outerside of the aluminum sheet "column 2"
\$     ssid      type
2         1
\$    flcid     fmult     tlcid     tmult       loc
03.4022E-11         0    273.15
*BOUNDARY_CONVECTION_SET
\$ convection boundary on outerside of the aluminum sheet "column 3"
\$ which substitutes radiation by defining hrad trough a curve
\$     ssid
3
\$    hlcid     hmult     tlcid     tmult       loc
-101         1         0    273.15
*BOUNDARY_CONVECTION_SET
\$ convection boundary on outerside of the aluminum sheet "column 4"
\$ which substitutes radiation by defining hrad trough a function
\$     ssid
4
\$    hlcid     hmult     tlcid     tmult       loc
201         1         0    273.15
*BOUNDARY_CONVECTION_SET
\$ convection boundary on outerside of the aluminum sheet "column 5"
\$     ssid
5
\$    hlcid     hmult     tlcid     tmult       loc
0      0.01         0    273.15
\$ convection boundary on outerside of the aluminum sheet "column 5"
\$     ssid      type
5         1
\$    flcid     fmult     tlcid     tmult       loc
03.4022E-11         0    273.15
*BOUNDARY_TEMPERATURE_SET
\$ temperature inside
\$  nid/sid     tlcid     tmult       loc    tdeath    tbirth
1         0    293.15
*DEFINE_FUNCTION
\$ hrad as a function of temperature in K, hrad is used to calculate heat
\$ convection, which substitutes radiation.
float func_hrad(float x,float y,float z,float vx,float vy,float vz,float temp,
float tinf,float time)
{
float emissivity=0.6;
float sb=5.6704E-11;
}
*DEFINE_CURVE
\$ hrad as a function of temperature in K, hrad is used to calculate heat
\$ convection, which substitutes radiation
\$     lcid      sidr       sfa       sfo      offa      offo    dattyp
101         0         1         1         0         0         0
\$   Tfilm    ,    hrad
2.6157500E+02,2.4404124E-03
...,...
...
\$
*END```