Release 11.0 Documentation for ANSYS
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| Matrix or Vector | Shape Functions | Integration Points |
|---|---|---|
| Conductivity Matrix | None (nodes may be coincident) | None |
The two-surface radiation equation (from (Equation 6–13)) that is solved (iteratively) is:
| (14–243) |
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 14–243) is expanded as:
| (14–244) |
and then rewritten as:
| (14–245) |
where the subscripts n and n-1 refer to the current and previous iterations, respectively. It is then recast into finite element form:
| (14–246) |
with
| (14–247) |
The basic equation is:
| (14–248) |
instead of (Equation 14–243). This form leads to
| (14–249) |
instead of (Equation 14–247). And, hence the matrix (Equation 14–246) becomes:
| (14–250) |
If the emissivity is input on a temperature dependent basis, (Equation 14–247) is rewritten to be:
| (14–251) |
where:
 |
 |
 |
| Toff = offset temperature (input on TOFFST command) |
(Equation 14–249) is handled analogously.
