13.31. LINK31 - Radiation Link

Matrix or VectorShape Functions Integration Points
Conductivity Matrix None (nodes may be coincident)None

13.31.1. Standard Radiation (KEYOPT(3) = 0)

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)

13.31.2. Empirical Radiation (KEYOPT(3) = 1)

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)

13.31.3. Solution

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.