From the Glansdorff–Prigogine local potential in non-equilibrium thermodynamics (1)† (2), a variational principle for a thin film incompressible flow with viscous dissipation is formulated as the basis of a finite-element method, which is applied to solve the energy equation. Temperature distributions in tapered land and parallel oil films for infinitely wide bearings are obtained by digital computer. The application of the finite-element method in a three-dimensional oil film with side leakage is also discussed.
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