Dissipation
Due to the viscous friction, heat will be produced in the lubricating film. In some cases, it may be important to couple the flow in the bearing to a heat transfer analysis. In the Hydrodynamic Bearing interface, the dissipated energy per volume is computed. It is available in a variable named hdb.Qvd, which you can use as a heat source in a thermal analysis.
Viscous dissipation per unit volume in a flow can be calculated in terms of the strain rate and stress tensors:
with
and
For a thin-film flow approximation (neglecting higher orders of h/l) the rate of deformation and stress tensor in the local system are approximated as
and
Therefore, in a thin-film flow the viscous dissipation is approximately given by
Substituting the velocity expression in terms of the pressure in the film and integrating across the film thickness the heat dissipation per unit area of the film is given by
where
Here, hb is the height of the bearing from the reference surface, and hj is the height of the journal from the reference surface. Lsj and Lsb are the slip lengths at the journal and bearing surfaces, respectively. (vj − vb)t is the tangential velocity component of the relative journal velocity with respect to the bearing in the film plane.
Therefore, viscous dissipation per unit volume will be approximately given by