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The purpose of this paper is to present the problem of three‐dimensional flow of a fluid of constant density forced through the porous bottom of a circular porous slider moving laterally on a flat plate.

The transformed nonlinear ordinary differential equations are solved via the homotopy perturbation method (HPM) for small as well as moderately large Reynolds numbers. The convergence of the obtained HPM solution is carefully analyzed. Finally, the validity of results is verified by comparing with numerical methods and existing numerical results.

Close agreement of the two sets of results is observed, thus demonstrating the accuracy of the HPM approach for the particular problem considered.

Interesting conclusions which can be drawn from this study are that HPM is very effective and simple compared to the existing solution method, able to solve problems without using Padé approximants and can therefore be considered as a clear advantage over the N.M. Bujurke and Phan‐Thien techniques.

The purpose of this study is to present a theoretical investigation of the effects of cavitation and couple stress on the squeeze film behavior between an anisotropic poroelastic rigid disc and a sinusoidally oscillating rigid disc.

Based on the microcontinuum theory of Vijay Kumar Stokes and the Elrod–Adam algorithm, the non-Newtonian Reynolds equation coupled with modified Darcy's law for lubricant flow through the porous disc is derived. This numerical study includes the continuity of tangential velocity at the porous–fluid interface and the effects of percolation of the polar additives into the anisotropic porous disc.

The effects of couple stress, oscillating amplitude, percolation additives, permeability and anisotropic permeability on the squeeze film characteristics are discussed. It is found that both the percolation effect of the lubricant additives and the anisotropic structure of the porous surface reduce the flow in the porous disc, resulting in a decrease in pressure. It is also observed that cavitation effects are more pronounced for Newtonian fluids than couple stress fluids.

The results of this study can be used to design a variety of engineering applications such as bearings, wet clutches and non-contact mechanical seals.

To study the combined effects of permeability and couplestresses on the performance characteristics of a secant‐shaped porous slider bearing lubricated with Stokes couplestress fluid.

The modified Reynolds type equation governing the fluid film pressure is derived on the basis of Stokes microcontinuum theory of couplestress fluids by using Beavers‐Joshep slip boundary conditions at the fluid‐porous interface. The modified Reynolds equation is solved analytically and closed form expressions are obtained for the fluid film pressure, load carrying capacity, frictional force and centre of pressure.

The bearing characteristics are computed for various values of the couple stress parameter, slip parameter and the permeability parameters. It is found that, the effect of couple stress is to increase the load carrying capacity and to decrease the coefficient of friction as compared to the Newtonian case. However, the effect of permeability parameter is to decrease the load carrying capacity. It is also found that, the effect of couple stresses is to shift the center of pressure towards the outlet edge.

The end effects are neglected in the analysis and these can be included in the study by considering full three‐dimensional problem.

Reduction in the load carrying capacity due to the presence of porous facing can be compensated by the use of lubricants containing additives of proper size. As a result the bearing performance can be improved.

This paper provides closed form expressions for the bearing characteristics and are analyzed with respect to non‐dimensional parameters, viz. couplestress parameter, slip parameter and permeability parameter. This paper offers help to design engineers to design efficient bearing systems.

The purpose of this paper is to study the laminar boundary layer flow between a stationary nonporous disk and a porous rotating disk, both being immersed in large amount of fluid.

The governing nonlinear momentum equations in cylindrical polar coordinates together with relevant boundary conditions are reduced to a system of coupled nonlinear ordinary differential equations (NODEs) using similarity transformations. The resulting coupled NODEs are solved using computer-extended series solution and homotopy analysis method.

The analytical solutions are explicitly expressed in terms of recurrence relation for determining the universal coefficients. The nature and location of singularity which restricts the convergence of series is analyzed by using Domb–Sykes plot. Reversion of series is used for the improvement of series. The region of validity of series is extended for much larger values of Reynolds number (R), i.e. R = 6 to 15.

The resulting solutions are compared with earlier works in the literature and are found to be in good agreement.

This paper aims to study the effects of surface roughness on the characteristics of squeeze film lubrication between curved annular plates.

The modified Reynolds type equation governing the fluid film pressure is derived. The stochastic method for rough surfaces developed by Christensen is to derive stochastic type equation and has been solved for two types of one‐dimensional roughness patterns. Closed form expressions of mean squeeze film pressure and mean load carrying capacity are obtained.

The bearing characteristics are computed for various values of roughness parameter. It is found that the effect of radial (circumferential) roughness pattern is to shift the point of maximum pressure towards the inlet (outlet) edge and also observe that the mean load‐carrying capacity increases (decreases) for the circumferential (radial) roughness pattern compared with the corresponding smooth case, for both concave and convex pad geometries.

The analysis is useful in obtaining suitable mathematical model of physical problems. The one which we have considered here is the idealized form of functioning of bearings in general. Analysis of finer models requires pure numerical schemes, for which the present model is a base.

Findings of the present paper have applications in machine elements like clutch plates and collar bearings.

Inclusions of surface roughness effect on the characteristics of bearings are original contributions in tribology.

The aim of this paper is to investigate the effect of surface roughness on the squeeze film characteristics of long porous partial journal bearings with couple stress fluids as lubricant.

The Stokes couple stress fluid model is included to account for the additives effects of lubricant. The Christensen's stochastic method developed for the hydrodynamic lubrication of rough surfaces is used to derive the stochastic Reynolds type equation accounting for the surface roughness and couple stresses. In the context of Christensen's stochastic theory for the hydrodynamic lubrication of rough surfaces, two types of one‐dimensional surface roughness (longitudinal and transverse) patterns are considered. The non‐linear first order differential equation governing the journal center movement is solved numerically by using the fourth order R‐K method.

From the numerical computations of the results, it is found that, the effect of couple stresses is to increase the load carrying capacity and also the response time. The effect of surface roughness is to increase (decrease) the load carrying capacity and the response time for transverse (longitudinal) roughness pattern. However, the effect of permeability parameter is to decrease the load carrying capacity and also to decrease the response time as compared to the solid case.

The original findings on the combined effects of surface roughness and couple stresses on the squeeze film characteristics of long porous partial journal bearing are of use to the bearing designers.

In the application of hydrostatic double-layered porous journal bearings, misalignment of bearing systems is a major problem. On the other hand, the use of coupled-stress fluid as a lubricant is more practical in the present days. Furthermore, in case of porous bearing, neglecting slip effect and percolation effect of additives into the pores may lead to erroneous result. Hence, this paper aims to address the effect of journal misalignment and coupled-stress lubricant on the steady-state film pressure of the double-layered porous journal bearing with tangential velocity slip and percolation effect.

First, considering the tangential velocity slip, the most general modified Reynolds type equation has been derived for the film region and the governing equations for flow in the coarse and fine layers of porous medium, incorporating the percolation effect for a double-layered porous bearing. Here, considering the misalignment caused by shaft displacement. Film thickness expression established considering the effect of misalignment. Steady-state film pressures are obtained by solving modified Reynolds equation based on the coupled-stress lubrication theory. Effects of journal misalignment and coupled-stress lubricant on the pressure profiles in the film region are discussed and demonstrated in the graphical form.

In this paper, effects of journal misalignment and coupled-stress lubricant on the pressure profiles in the film region are obtained. In general, higher degree of misalignment gives higher steady-state pressure value in the film region, and this pressure increases due to increase in coupled-stress parameter up to a certain limit.

To the best of the author’s knowledge, there is no literature available, so far, that addresses the analysis of the steady-state pressure in the film region of a doubled–layered porous journal bearing under misaligned condition with coupled-stress lubricant. But in this paper all these points are included, which makes this article valuable in design purpose.

The purpose of this paper is to investigate some multiple solutions for carbon nanotubes (CNTs) in a porous channel with changing walls. Moreover, the intention of the study is to examine the physicochemical and rheological properties of titania and CNTs.

The mathematical modeling is performed for the laws of conservation of mass, momentum and energy profiles. Governing partial differential equations are transformed into ordinary differential equations by applying suitable similarity transformation and then solved numerically with the help of shooting technique.

The effects of different physical parameters on the rheology of nanofluids are discussed graphically and numerically, in order to make the analysis more interesting. The present study revealed that multiple solutions of nanofluids in a channel with changing walls are obtained only for the case of suction.

Some new branches of the solution for nanofluids in a channel with changing walls are obtained in this research, which has never been reported before. Combined effects of physicochemical and rheology of titania and carbon nanotubes are investigated briefly. The effects of physical parameters on velocity and temperature profile are examined in detail which is more realistic than real-world problem.

The purpose of this paper is to analyse the static performance characteristics of lobe journal bearings lubricated with a micropolar fluid, considering effect of non‐circularity. Number of lobes and their preload value are the non‐circularity parameters considered in the present study. The bearings undertaken for the investigation are two, three and four‐lobe symmetric journal bearings with finite width.

For this purpose, modified form of Reynolds equation is derived, based on Eringen's micropolar fluid theory and it is solved numerically using finite element method (FEM). The effect of the non‐circularity parameters of bearings on the steady‐state performance characteristics such as load carrying capacity, attitude angle, coefficient of friction and side leakage flow are presented and discussed.

The results show that the number of lobes and their preload value can influence the performance of lobe bearings. It is seen that, in order to provide certain improvement over simple cylindrical bearings, the non‐circularity parameters of lobe bearings must be chosen correctly. There is no single optimum profile for multi‐lobe bearing application.

Lobe bearings, compared with simple circular bearings, offer several geometric parameters to designers. These parameters must be chosen correctly, so that the requirements of a specific application can be fulfilled.

In the present paper, the squeeze film lubrication between anisotropic porous rectangular plates with lubricants containing polar additives has been studied. The lubricants containing additives has been modelled as a Stokes couple stress fluid. The more realistic Beavers‐Joseph slip boundary conditions are used to derive the most general form of Reynolds equation, which account for the effects due to the lubricant additives and the anisotropic nature of porous material. The eigen type of expressions are obtained for the fluid film pressure, load carrying capacity and squeeze film time. It is observed that the effect of the lubricant additives is to increase the load carrying capacity and the squeeze film time as compared to the Newtonian lubricants. Further for anisotropic porous surface, the maximum load carrying capacity is attained for the rectangular (non‐square) plates.