Numerical Solution of the MHD Reynolds Equation for Squeeze-Film Lubrication between Porous and Rough Rectangular Plates

The present theoretical study investigates the effects of surface roughness and couple-stress fluid between two rectangular plates, of which an upper rough plate has a roughness structure and the lower plate has a porous material in the presence of transverse magnetic field. The lubricant in the gap is taken to be a viscous, incompressible, and electrically conducting couple-stress fluid. This gap is separated by a film thickness H which is made up of nominal smooth part and rough part. The modified Reynolds equation in the film region is derived for one-dimensional longitudinal roughness structure and solved numerically using multigrid method. The numerical results for various physical parameters are discussed in terms of pressure distribution, load capacity, and squeeze film time of the bearing surfaces. Our results show that, the pressure distribution, load capacity and squeeze film time are predominant for larger values of Hartman number and roughness parameter, and for smaller values of couple-stress parameters when compared to their corresponding classical cases

Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness

Impact of temperature-dependant viscosity and thermal conductivity on MHD boundary layer flow of two-phase dusty fluid through permeable medium

The distribution of solid particles in a fluid leading to two-phase nature as in micro-propulsion, aerosol filtration, conveying of powdered materials, petroleum industry and lunar ash flow can be described as an open question. In this study, boundary layer flow of an electrically conducting magnetohydrodynamic dusty fluid in a porous medium is presented. Fluid viscosity and thermal conductivity are assumed to be an inverse linear function of temperature. The governing nonlinear partial differential equations and their physically realistic boundary conditions are reduced into dimensionless form by using appropriate transformations. The resultant coupled system of equations is discretized using finite difference scheme and Thomas algorithm is implemented to solve the linear algebraic equation. A representative set of numerical results are plotted to visualize the impact of existing fluid interaction parameters. Skin-friction, heat and mass transfer coefficients are tabulated and results obtained are in good agreement with the literature. From this investigation, velocity, temperature and concentration fields are observed to be an increasing function in accordance with the raise in both viscosity variation parameter (θr) and thermal conductivity variation parameter (θc). This computation illustrates that the friction factor coefficient is found to be less for low thermal expansion coefficient irrespective of all emerging parameters of the flow. Furthermore, enhancement in θr reduces the heat transfer rate and strengthens the mass transfer rate whereas the reverse trend is observed for θc. Keywords: Boundary layer, Dusty fluid, Variable viscosity, Variable thermal conductivity, Heat and mass transfe

Numerical Study of Surface Roughness and Magnetic Field between Rough and Porous Rectangular Plates

This paper theoretically examines the combined effects of surface roughness and magnetic field between two rectangular parallel plates of which the upper plate has roughness structure and the lower plate has porous material in the presence of transverse magnetic field. The lubricating fluid in the film region is assumed to be Newtonian fluid (linearly viscous and incompressible fluid). This model consists of mathematical formulation of the problem with appropriate boundary conditions and solution numerically by finite difference based multigrid method. The generalized average modified Reynolds equation is derived for longitudinal roughness using Christensen’s stochastic theory which assumes that the height of the roughness asperity is of the same order as the mean separation between the plates. We obtain the bearing characteristics such as pressure distribution and load carrying capacity for various values of roughness, Hartmann number, and permeability parameters. It is observed that the pressure distribution and load carrying capacity were found to be more pronounced for increasing values of roughness parameter and Hartmann number; whereas these are found to be decreasing for increasing permeability compared to their corresponding classical cases. The physical reasons for these characters are discussed in detail