| Matrix or Vector | Shape Functions | Integration Points |
|---|---|---|
| Conductivity Matrix | None (nodes may be coincident) | None |
The two-surface radiation equation (from Equation 6–14) that is solved (iteratively) is:
 | (13–18) |
where:
| Q = heat flow rate between nodes I and J (output as HEAT RATE) |
| σ = Stefan-Boltzmann constant (input as SBC on R command) |
| ε = emissivity (input as EMISSIVITY on R or EMIS on MP command) |
| F = geometric form factor (input as FORM FACTOR on R command) |
| A = area of element (input as AREA on R command) |
| TI, TJ = absolute temperatures at nodes I and J |
The program uses a linear equation solver. Therefore, Equation 13–18 is expanded as:
 | (13–19) |
and then rewritten as:
 | (13–20) |
where the subscripts n and n-1 refer to the current and previous iterations, respectively. It is then recast into finite element form:
 | (13–21) |
with
 | (13–22) |
The basic equation is:
 | (13–23) |
instead of Equation 13–18. This form leads to
 | (13–24) |
instead of Equation 13–22. And, hence the matrix Equation 13–21 becomes:
 | (13–25) |
If the emissivity is input on a temperature dependent basis, Equation 13–22 is rewritten to be:
 | (13–26) |
where:
|
 |
|
| Toff = offset temperature (input on TOFFST command) |
Equation 13–24 is handled analogously.