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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.

Parallel magnetic susceptibility temperature dependence of the high-TC superconducting parent compound La CuO is calculated in both antiferromagnetic (AFM) and paramagnetic phase. By making use of the quantum Heisenberg three-dimensional AFM model including the in-plane spin anisotropy, the calculation is performed within the framework of three different theories: Green’s function theory in random-phase approximation (RPA), linear spinwave (LSW) theory and mean-field (MF) theory. The results suggest that at low temperatures quantum spin fluctuations play an important role, while at the temperatures above the critical one short-range correlations have a great impact on the behavior of the system. This leads to the discrepancy between RPA and MF results, since the later neglects the above phenomena. Further, LSW theory expectedly agrees with RPA results only at low temperatures where the magnon interactions are negligible. Comparison to the theoretical and experimental results quoted in literature confirms that RPA method presents the most appropriate method among the applied ones, suggesting that this approach is satisfactory in the case of the parallel magnetic susceptibility, while in order to reproduce the transversal one, spin-orbit coupling must be included.