The effects of angle of convergence on the shape and thickness of the core are analyzed theoretically by considering variable film thickness in an externally pressurized circular thrust bearing. Using the assumptions of the lubrication theory, modified Reynold’s equation and the governing equations are obtained. Using the boundary conditions of the problem in the constitutive equations we get the velocity of the core region as well as flow region. By considering the equilibrium of an element in the yield surface, an algebraic equation to determine the thickness of the yield surface is derived. Numerical solutions are obtained for the thickness of yield surface and velocities for various values of Bingham Numbers and the angle of convergence.
In the present theoretical investigation, the combined effects of fluid inertia forces and sinusoidal injection of the Bingham lubricant, on the performance of an externally pressurized thrust bearing with circular geometry are studied. Using the conventional two-constant Bingham model and by adopting the method of averaging inertia terms, the reduced Navier-Stokes equations are modified and numerical solutions have been obtained for the bearing performances such as the pressure distribution and the load carrying capacity for different values of Bingham number, Reynolds number, time and amplitude. The effects of fluid inertia forces and the non-Newtonian characteristics of the Bingham lubricant on the bearing performances for different sinusoidal conditions are discussed.
The combined effects of fluid inertia and viscous forces of a Herschel-Bulkley lubricant in an externally pressurized thrust bearing with circular geometry have been analyzed theoretically. Although the researchers of the past, laid out a foundation for the hydrodynamic lubrication, modern researchers intend to use non-Newtonian fluids characterized by a yield-value, such as Bingham, Casson and Herschel-Bulkley fluids as lubricants. More over, Tribologists emphasize a fact that in order to analyze the performance of the bearings adequately, it is necessary to consider the combined effects of fluid inertia and viscous forces of non-Newtonian lubricants. Therefore, in this research article, the combined effects of fluid inertia and viscous forces have been investigated theoretically in an externally pressurized thrust bearing with circular geometry using Herschel-Bulkley fluid as lubricant. The shape and extent of the core, along the radius, have been determined numerically for various values of the Herschel-Bulkley number and the power-law index. Using the appropriate boundary conditions, the velocity distributions in the flow and the core regions have been obtained. By considering the equilibrium of an element of the core in the fluid, the modified pressure gradient has been evaluated and thereby the film pressure and the load capacity of the bearing have been obtained numerically for different values of Reynolds number, Herschel-Bulkley number and power-law index. The effects of the inertia forces and the non-Newtonian characteristics of the lubricant, on the bearing performances have also been discussed.
This work analyses the entrance region flow of Bingham nanofluids in cylindrical concentric annuli. In this discussion, water is used as the base fluid which is embedded with the silver(Ag) and copper(Cu) nanoparticles coalescing with Bingham fluid. The investigation has been carried out by rotating the inner cylinder, while the outer cylinder is assumed to be at rest. A finite-difference analysis is used to obtain the axial, radial, tangential velocity components and the pressure along the radial direction. With the Prandtl's boundary layer assumptions, the continuity and momentum equations are solved iteratively using a finite difference method. Computational results are obtained for various non-Newtonian flow parameters, different volume fraction parameters and geometrical considerations. This work's main interest is to study the development of velocity profiles and pressure drop in the entrance region of the annuli. The present results are compared with the results available in the literature for various particular cases and it is found to be in good agreement.
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