In 3D models, the bulk temperature may be evaluated along an edge of the tube in the direction of the flow, by using the built-in diskint(R,expr,tol) operator. When applied to an edge in 3D models, this operator integrates an expression expr over a disk of radius R, perpendicular to the selected edge. A numerical tolerance parameter tol is also available to adjust the numerical precision.

In the evaluation of the bulk temperature, the radius R should be chosen large enough to encompass the tube cross section, but not too large regarding numerical precision.

If the evaluation disk overlaps other domains, the evaluation may be restricted to the domain of interest by adding a test on the dom variable.

The evaluation of the tangential velocity over the cross section requires to access the vector tangent to the edge, in the computational domain. However, the tangent vectors t1 and t2 are defined on boundaries only. By applying the general extrusion operator genext1 on the edge, with a mapping to the domain, the tangential vector genext1(t1) is defined all over the cross section, and can be used in the diskint operator expression.

where ut = u*genext1(t1x)+v*(genext1(t1y)+w*genext1(t1z), i is the domain entity number, and the tolerance tol should be specified.