A global method for the solution of thermohydrodynamic problems is proposed for the analysis of lubricated contacts with non-newtonian fluids. A set of algebraic equations is obtained after introducing the weak form of the energy equation and a modified generalized equation for thin fluid flows. This last equation represents a new formulation for lubrication with non-newtonian fluids. The establishment of this equation is presented below along with several tests including explicit and implicit rheological laws with some comments on the effect of the different parameters which occur in the study.

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