This paper presents the analytical solutions to laminar flow of MHD Newtonian and non-Newtonian power-law fluids in the entrance region of channels. The boundary layer growth and velocity profile of developing flow in a two-dimensional channel, under the influence of a uniform magnetic field, are investigated. The direction of the magnetic field is assumed perpendicular to the flow. For each case, a novel and useful non-dimensional correlation for computing the magnetic entrance length is proposed, using the integral equations method. In addition, the effect of different parameters on the magnetic entrance length, boundary layer thickness and thus core velocity and pressure loss are studied. It was found that with the increase of the Hartmann number, the entrance length declined. Furthermore, the entrance length decreases while the powerlaw index and magnetic interaction parameter increase. As well as, the results have shown that the augmentation of the magnetic interaction parameter leads to greater pressure drop in comparison with the hydrodynamic flow. Keywords Entrance length Á Integral method Á MHD channel Á Power-law fluid 1 Introduction Magnetohydrodynamics (MHD) apparatus such as channels in reactors, MHD flow meters, MHD generators, pumps, etc., have a significant role in engineering applications. The distance along the channel length, where the centerline velocity reaches 99.9% of its final magnetic fully Technical Editor: Cezar Negrao.

No abstract

Abstract. The focus of the present work is on the investigation of the separation point and its relative location in a circular diffuser carrying incompressible laminar flow in the presence of a non-uniform external magnetic field. Two different approaches are deployed in the present analysis. In the first approach, a similarity transform is applied to reduce the momentum equation to the nonlinear ordinary differential equation (ODE). The ODE is solved by a dual integral–numerical method and the separation position is directly determined. In this combined numerical–integral methodology, the integration is applied followed by a numerical method. In the second approach, the equation is solved by the least square method (LSM), and the separation position is indirectly specified. In this study it is shown that the magnetic field intensity can be manipulated to postpone the separation such that it could be eliminated totally. Comparing the results yields a good agreement. It has been concluded that by increasing the magnetic field intensity, as the Lorentz force increases, increased shear stress on the wall and delay in the occurrence of the separation position are observed.

No abstract

In this paper, to study the incompressible fully developed flow of a non-Newtonian fourth grade fluid in a flat channel under an externally applied magnetic field, an appropriate analysis has been performed considering the slip condition on the walls. The governing equations, Ohm's law, continuity and momentum for this problem are reduced to a nonlinear ordinary form. The nonlinear equation with robin mixed boundary condition is solved with collocation (CM) and least square (LSM) methods. The effects of parameters such as non-Newtonian, magnetic field and slip parameters on dimensionless velocity profiles will be discussed. In the end, the results could bring us to this conclusion that collocation and least square methods can be used for solving nonlinear differential equations with robin mixed condition.