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The present study investigates the combined influence of the nanoparticles and uniform magnetic field applied on the slip blood flow. Blood conveyed through the hollow arterial tube is described as a third-grade non-Newtonian fluid with time dependent viscosity and formulated by the second-order nonlinear ordinary differential equations. Therefore, the regular perturbation method as an approximate analytical method can be applied providing a solution to the coupled system of equations. The results obtained from the solution are used to show the effect of parameters including the magnetic parameter, the viscous dissipation and the pressure gradient on the slip blood flow. Analytical results reveal augmentation of the pressure gradient and the magnetic parameter decrease the velocity value whilst the viscous dissipation augmentation increases the temperature. Also, the comparison between the analytical results with the results obtained from numerical solution shows the good agreement.

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.

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