LINK31
Radiation
Link
LINK31 Element Description
LINK31 is a uniaxial element which models the radiation heat flow rate between two points in space. The link has a single degree of freedom, temperature, at each node. The radiation element is applicable to a 2D (plane or axisymmetric) or 3D, steady-state or transient thermal analysis.
An empirical relationship allowing the form factor and area to multiply the temperatures independently is also available. The emissivity may be temperature dependent. If the model containing the radiation element is also to be analyzed structurally, the radiation element should be replaced by an equivalent (or null) structural element. See LINK31 in the Mechanical APDL Theory Reference for more details about this element.
LINK31 Input Data
The geometry, node locations, and the coordinate system for this radiation element are shown in Figure 31.1: LINK31 Geometry. The element is defined by two nodes, a radiating surface area, a geometric form factor, the emissivity, and the Stefan-Boltzmann constant (SBC). For axisymmetric problems, the radiation area should be input on a full 360° basis.
The emissivity may be constant or temperature (absolute) dependent. If it is constant, the value is input as a real constant. If it is temperature dependent, the values are input for the material property EMIS and the real constant value is used only to identify the material property number. In this case the MAT value associated with element is not used. EMIS defaults to 1.0.
The standard radiation function is defined as follows:
q = σ εFA(T(I)4 - T(J)4)
where:
| σ = Stefan-Boltzmann Constant (SBC) |
| (defaults to 0.119 x 10-10 (BTU/Hr*in2* °R4) |
| ε = emissivity |
| F = geometric form factor |
| A = area (Length)2 |
| q = heat flow rate (Heat/Time) |
The nonlinear temperature equation is solved by a Newton-Raphson iterative solution based on the form:
[(T(I)2 + T(J)2)(T(I) + T(J))]p(T(I) - T(J))
where the [ ]p term is evaluated at the temperature of the previous substep. The initial temperature should be near the anticipated solution and should not be zero (that is, both TUNIF and TOFFST should not be zero).
An empirical radiation function of the following form may also be selected with KEYOPT(3):
q = σ ε(FT(I)4 - AT(J)4)
where F and A are arbitrary input constants.
A summary of the element input is given in "LINK31 Input Summary". A general description of element input is given in Element Input.
LINK31 Input Summary
- Nodes
I, J
- Degrees of Freedom
TEMP
- Real Constants
AREA - Radiating surface area FORM FACTOR - Geometric form factor EMISSIVITY - Emissivity (If EMISSIVITY = -n, use material n for emissivity vs. temperature definition) SBC - Stefan-Boltzmann constant - Material Properties
MP command: EMIS (required only if EMISSIVITY = -N)
- Surface Loads
None
- Body Loads
None
- Special Features
- KEYOPT(3)
Radiation equation:
- 0 --
Use standard radiation equation
- 1 --
Use empirical radiation equation
The Stefan-Boltzmann constant (SBC) defaults to 0.1190E-10 with units of Btu, hr, in, °R (or °F if TOFFST is used)
LINK31 Output Data
The solution output associated with the element is in two forms:
Nodal temperatures included in the overall nodal solution
Additional element output as shown in Table 31.1: LINK31 Element Output Definitions
The heat flow rate is positive from node I to node J. A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.
The Element Output Definitions table uses the following notation:
A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file jobname.out. The R column indicates the availability of the items in the results file.
In either the O or R columns, “Y” indicates that the item is always available, a letter or number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.
Table 31.1: LINK31 Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| EL | Element Number | Y | Y |
| NODES | Nodes - I, J | Y | Y |
| MAT | Material number | Y | Y |
| AREA | AREA | Y | Y |
| XC, YC, ZC | Location where results are reported | Y | 1 |
| EMIS(I, J) | Emissivity - I, J | Y | Y |
| TEMP(I, J) | Temperatures - I, J | Y | Y |
| HEAT RATE | Heat flow rate from node I to node J | Y | Y |
Available only at centroid as a *GET item.
Table 31.2: LINK31 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 31.2: LINK31 Item and Sequence Numbers:
- Name
output quantity as defined in the Table 31.1: LINK31 Element Output Definitions
- Item
predetermined Item label for ETABLE command
- E
sequence number for single-valued or constant element data
LINK31 Assumptions and Restrictions
If the default Stefan-Boltzmann constant is used, the units associated with this element are Btu, inches, hours and °R (or °F + TOFFST). Other data input for this analysis must be consistent with this set of units or an appropriate conversion factor should be included in the radiation element's real constants.
Nodes may or may not be coincident.
An iterative solution is required with this element.