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Application of finite element methods to thermohydrodynamic lubrication
Author(s) -
Huebner Kenneth H.
Publication year - 1974
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620080112
Subject(s) - finite element method , mathematics , mixed finite element method , galerkin method , extended finite element method , mathematical analysis , physics , thermodynamics
A finite element formulation is presented for the equations governing the steady thermohydrodynamic behaviour of liquid lubricated bearings. This formulation permits application of the iterative solution scheme to bearings of arbitrary geometry. A generalized Reynolds equation resulting from the combination of the mass and momentum conservation equations is cast into variational form and used to derive general finite element equations. The method of weighted residuals with Galerkin's criterion is used to generate finite element matrix equations for the thermal energy equation. In addition to the finite element formulation, a discussion of appropriate finite difference techniques is also given for problems without complex geometry. As an example, the formulations are applied to obtain numerical solutions for a three‐dimensional sector thrust bearing operating in the thermohydrodynamic regime. Pressure, velocity and temperature distributions are give, and the thermohydrodynamic solutions are compared with the results of classical isothermal theory.