Material Model for Heat-Transfer Analysis

The material type heat is used to specify linear and nonlinear material parameters for heat conduction, heat convection, and heat radiation elements. For heat conduction, isotropic and orthotropic materials are supported. Depending whether heat conduction elements or heat convection and heat radiation 'overlay' elements reference the material, different parameters may need to be specified.

material id type heat
  k|k1|k2|k3 ...
  [specific_heat ...]
  [density v]
  h_c ...
  diffuse_reflectivity v
  emissivity v
  stefan_boltzmann_constant v
  radiation_reference_temperature v
end

1. Heat Conduction Parameters

k|k1|k2|k3 ...

Specifies the value v of the conductivity coefficient in material directions 1, 2 and 3. If k is specified, this means k1=k2=k3=k.

The conductivity can be specified as a constant, as a set of support points for a linear or cubic-spline interpolation, or as a Python expression.

k|k1|k2|k3 v
k|k1|k2|k3 interpolated linear|cubic flist
k|k1|k2|k3 function f

For the interpolation, the temperatures and corresponding conductivity coefficients must be specified with a list:

k interpolated cubic [
    -100.0 8.95 173.15 8.95 273.15 11.5 1623.15 46. 3623.15 51. 5623.15 51.
]

If the conductivity is specified as a Python expression, that expression must be specified as a string, where t is the temperature:

k function '0.3 * t**2'
c_p ...

Defines the specific heat (required for non-stationary analysis). The specific heat can be specified as a constant, as a set of support points for a linear or cubic-spline interpolation, or as a Python expression.

c_p v 
c_p interpolated linear|cubic flist 
c_p function f

density v

Specifies the value v of the density of the material (required for non-stationary analysis).

2. Heat Convection Attributes

h_c ...

Specifies the convection coefficient. The convection coefficient can be specified as a constant, as a set of support points for a linear or cubic-spline interpolation, or as a Python expression.

h_c  v 
h_c interpolated linear|cubic flist 
h_c function f

3. Heat Radiation Attributes

diffuse_reflectivity v

Specifies the fraction of incident radiation reflected by the radiating surfaces. v must be in the range of 0.0 to 1.0. The reflection is supposed to be diffuse. Default value is 0.0, i.e. all incoming radiation is absorbed.

emissivity v

Specifies the ratio of the energy radiated by the material to the energy radiated by a black body at the same temperature. v must be in the range of 0.0 to 1.0. Default value is 0.0, i.e. the material does not radiate.

stefan_boltzmann_constant v

Specifies the Stefan-Boltzmann constant, must be given according to the units used. Default is 5.6704e-8 for use with S.I. units.

radiation_reference_temperature v

Specifies the reference temperature for radiation into the void. Default is 0.0.

4. Example

material 1 type heat
  k 10.0
  c_p 1000.0
  radiation_reference_temperature 300.
  density 1000.
  emissivity 0.83
  stefan_boltzmann_constant 5.67e-8
end