A Quasi-Two-Dimensional Approach in Laminar Flow of Lubricating Oil and Grease

The overarching objective of the present study is to apply a quasi-two-dimensional approach to analyze the laminar flow of lubricating oil. Lubricating oils are non-Newtonian by nature. For these types of oils, the Sisko fluid model is the most suitable model of the nonlinear stress–strain relationship for these types of oils. It is hoped that by omitting the dependence of flow quantities in one direction, more qualitative information can be obtained on the characteristics of the purely three-dimensional boundary layer flow of lubricating oils. Some of the most familiar flow geometries discussed are steady flow over a flat plate, a corner of a wedge, and a stagnation region; steady flow in a convergent and divergent channel; and impulsively started flow over an infinite flat plate and semi-infinite flat plate. The governing equations of all flow geometries are transformed into nonlinear ordinary differential equations (ODE) using the free parameter transformation. The results are discussed briefly in the graphical presentation.