The element thermal gradients at the integration points are:
 | (6–29) |
where:
| {a} = thermal gradient vector (output as TG) |
| {L} = vector operator |
| T = temperature |
Using shape functions, Equation 6–29 may be written as:
 | (6–30) |
where:
| [B] = shape function derivative matrix evaluated at the integration points |
| {Te} = nodal temperature vector of element |
Then, the heat flux vector at the integration points may be computed from the thermal gradients:
 | (6–31) |
where:
| {q} = heat flux vector (output as TF) |
| [D] = conductivity matrix (see Equation 6–2) |
Nodal gradient and flux vectors may be computed from the integration point values as described in Nodal and Centroidal Data Evaluation.
