6.3. Heat Flow Evaluations

6.3.1. Integration Point Output

The element thermal gradients at the integration points are:

(6–23)

where:

{a} = thermal gradient vector (output as TG)
{L} = vector operator
T = temperature

Using shape functions, Equation 6–23 may be written as:

(6–24)

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:

(6–25)

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.

6.3.2. Surface Output

The convection surface output is:

(6–26)

where:

qc = heat flow per unit area due to convection
hf = film coefficient (input on SF or SFE commands)
TS = temperature at surface of model
TB = bulk temperature of the adjacent fluid (input on SF or SFE commands)


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