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

Analysis of the viscosity dependent parameters of couple stress fluid in porous parallel plates

Purpose: This paper aims to present a detailed analysis to explore the various properties of non-Newtonian couple stress lubricants between parallel porous plates. Design/methodology/approach: With reference to the theories based on micro-continuum analysis, a non-linear, non-Newtonian Reynolds type equation is arrived. The closed form solutions obtained clearly indicate the changes in pressure, load bearing capacity and response time because of variation in viscosity of couple stress fluid. Findings: It is observed that the viscosity variation factor greatly influences the change in pressure, load carrying capacity and squeezing time. Originality/value: It is observed that the nature of lubricants with suitable additives greatly helps in overcoming the adverse effect because of porous surface. Reynolds type equation is analysed using appropriate boundary conditions. The expression for pressure distribution arrived at in turn leads to the analysis of load bearing capacity and response time. © 2018, Emerald Publishing Limited