Unsteady pulsatile flow of blood through porous medium in an artery has been studied under the influence of periodic body acceleration and slip condition in the presence of magnetic field considering blood as an incompressible electrically conducting fluid. An analytical solution of the equation of motion is obtained by applying the Laplace transform. With a view to illustrating the applicability of the mathematical model developed here, the analytic explicit expressions of axial velocity, wall shear stress, and fluid acceleration are given. The slip condition plays an important role in shear skin, spurt, and hysteresis effects. The fluids that exhibit boundary slip have important technological applications such as in polishing valves of artificial heart and internal cavities. The effects of slip condition, magnetic field, porous medium, and body acceleration have been discussed. The obtained results, for different values of parameters into the problem under consideration, show that the flow is appreciably influenced by the presence of Knudsen number of slip condition, permeability parameter of porous medium, Hartmann number of magnetic field, and frequency of periodic body acceleration. The study is useful for evaluating the role of porosity and slip condition when the body is subjected to magnetic resonance imaging (MRI).

This work is concerned with the peristaltic transport of a Newtonian and non-Newtonian Maxwellian fluid in an axisymetric cylindrical tube filled with a homogenous porous medium, in which the flow is induced by traveling transversal waves on the tube wall. Like in peristaltic pumping, the traveling transversal waves induce a net flow of the liquid inside the tube. The viscosity as well as the compressibility of the liquid is taken into account. Modified Darcy's law has been used to model the governing equation. The present theoretical model may be considered as mathematical representation to the case of gall bladder and bile duct with stones and dynamics of blood flow in living creatures. The Navier–Stokes equations for an axisymmetric cylindrical tube are solved by means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the tube is small parameter. In the second order approximation, a net flow induced by the traveling wave is calculated for various values of the compressibility of the liquid, relaxation time and the permeability parameter of porous medium. The calculations disclose that the compressibility of the liquid, the permeability parameter of porous medium and non-Newtonian effects in presence of peristaltic transport have a strong influence of the net flow rate. Finally, the graphical results are reported and discussed for various values of the physical parameters of interest.

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AbstractIn the article, the effects of the thermal viscosity and magnetohydrodynamic on the peristalsis of nanofluid are analyzed. The dominant neutralization is deduced through long wavelength approximation. The analytical solution of velocity and temperature is extracted by using steady perturbation. The pressure gradient and friction forces are obtained. Numerical results are calculated and contrasted with the debated theoretical results. These results are calculated for various values of Hartmann number, variable viscosity parameter and amplitude ratio. It is observed that the pressure gradient is reduced with an increase in the thermal viscosity parameter and that the Hartmann number enhances the pressure difference.