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Thermally driven flow in a tall inclined cavity bounded by porous layers is studied analytically and numerically. A constant heat flux is applied for heating and cooling of two opposing walls of the cavity, while the other two are insulated. The Beavers—Joseph slip condition on velocity is applied at the interface between the fluid and porous layers. An analytical solution is obtained by assuming parallel flow in the core region of the cavity and a numerical solution by solving the complete governing equations. The flow and heat transfer variables are obtained in terms of the Rayleigh number, Ra, slip condition parameter N and angle of inclination of the cavity Φ. The critical Rayleigh numbers for the onset of convection in a layer heated from below are predicted for various hydrodynamic boundary conditions. The results for a fluid layer bounded by solid walls (N → ∞) and by free surfaces (N → 0) emerge from the present analysis as limiting cases.

The purpose of this study is to investigate the viscous shear effect on finite porous elastic journal bearings lubricated with non-Newtonian couple stress fluid.

Based on Stokes micro-continuum mechanics, the modified Reynolds equation including bearing deformation was derived. The porous flow was modeled by the complete Darcy–Brinkman equation. To show the viscous shear effects, bearing characteristics including load capacity and friction factor are compared to those obtained from Darcy model with Beavers–Joseph slip conditions (slip flow model [SFM]) by developing a computer program and discussed for different couple stress values, permeabilities and elastic deformation parameters.

It is found that the viscous shearing forces effects of the Brinkman model increase the load capacity and friction factor compared to those derived using SFM. Moreover, the couple stresses increase the load capacity while decreasing the friction factor for both models.

This study introduces for the first time the viscous effect on finite porous elastic journal bearings lubricated with couple stress fluid.

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.

This study aims to investigate the thermohydrodynamic (THD) and thermoelastohydrodynamic (TEHD) performance of an air-lubricated thrust bearing under different slip conditions, especially the slip length effect.

In this study, a new modified boundary slip model was established to investigate thrust bearing performance. The THD and TEHD bearing characteristic distribution was analyzed with fluid–thermal–structure interaction approach. The effect of the slip length on the bearing performance was studied using various bearing structure parameters.

The increased slip length changed the classical feature distribution of the film pressure and temperature. The sacrifice of the bearing load capacity effectively compensated for the aerodynamic thermal effect and friction torque under the slip condition. The TEHD model has a lower film pressure and load capacity than the THD model. However, it also has lower film temperature, lower friction torque and smaller Knudsen number (Kn).

The bearing THD and TEHD performances of the modified boundary slip model were compared with those of a traditional no-slip bearing. The results help to guide the selection of the bearing surface materials and processing technology of rotor and foil, so as to fully control the degree of slip and make use of it.

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.

This paper aims to provide a limited, but selective bibliography on modelling heat and mass transfer in composite fluid‐porous domains.

Since the pioneer study by Beavers and Joseph, the problem of interface continuity and/or jump conditions at a fluid‐porous interface has been of interest to the fluid mechanics and heat and mass transfer community. The paper is concerned both with numerical simulations of heat and fluid flow in such systems, and with the linear stability problems.

The one‐ and two‐domain formulations are equivalent. Using the Darcy‐Brinkman extension instead of the Darcy model reduces the number of ad hoc parameters in this configuration.

The problem of double diffusive convection has still to be solved and analyzed.

The discussion on the interface conditions is of great relevance to many industrial and practical situations.

The important question of the macroscopic formulation of the problem is tackled in the paper.

The purpose of this study is a numerical analysis of transient natural convection in a square partially porous cavity with a heat-generating and heat-conducting element using the local thermal non-equilibrium model under the effect of cooling from the vertical walls. It should be noted that this research deals with a development of passive cooling system for the electronic devices.

The domain of interest is a square cavity with a porous layer and a heat-generating element. The vertical walls of the cavity are kept at constant cooling temperature, while the horizontal walls are adiabatic. The heat-generating solid element is located on the bottom wall. A porous layer is placed under the clear fluid layer. The governing equations, formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions, are solved using implicit finite difference schemes of the second order accuracy. The governing parameters are the Darcy number, viscosity variation parameter, porous layer height and dimensionless time. The effects of varying these parameters on the average total Nusselt number along the heat source surface, the average temperature of the heater, the fluid flow rate inside the cavity and on the streamlines and isotherms are analyzed.

The results show that in the case of local thermal non-equilibrium the total average Nusselt number is an increasing function of the interphase heat transfer coefficient and the porous layer thickness, while the average heat source temperature decreases with the Darcy number and viscosity variation parameter.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady natural convection within a partially porous cavity using the local thermal non-equilibrium model in the presence of a local heat-generating solid element. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer in enclosures with local heat-generating heaters and porous layers, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

This paper aims to advance the squeeze film characteristics of long partial journal bearings with couple stress fluid studied by Lin to include the effect of permeability on the squeeze film lubrication of long partial porous journal bearings with couple stress fluids.

A semi‐analytical and semi‐numerical solution for the squeeze film lubrication of long porous partial journal bearings lubricated with couple stress fluid is presented in the paper. The modified Reynolds equation governing the fluid film pressure is derived. The modified Reynolds equation is solved analytically and closed form expressions for the squeeze film pressure and load carrying capacity are presented. The first‐order non‐linear equation for the time‐height relation is solved numerically with the given initial condition. The effect of couple stresses and permeability on the squeeze film characteristics are discussed.

It is found that the effect of couple stresses is to increase the load carrying capacity and to lengthen the squeeze film time as compared to the corresponding Newtonian case. The effect of permeability is to reduce the load carrying capacity and to decrease the squeeze film time as compared to the corresponding solid case.

In the design of porous partial journal bearings, the reduction in the load carrying capacity and the response time can be compensated by the use of lubricants with proper microstructures by which the bearing life can be increased.