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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.

Peristaltic pumping induced by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid mixed with rigid spherical particles is investigated theoretically taking the slip effect on the wall into account. A perturbation solution is obtained which satisfies the momentum equations for the case in which amplitude ratio (wave amplitude/channel half width) is small. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms and the slip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth-order terms yield the Poiseuille flow and the first-order terms give the Orr-Sommerfeld equation. The results show that the slip conditions have significant effect within certain range of concentration. The phenomenon of reflux (the mean flow reversal) is discussed under slip conditions. It is found that the critical reflux pressure is lower for the particle-fluid suspension than for the particle-free fluid and is affected by slip condition. A motivation of the present analysis has been the hope that such theory of two-phase flow process under slip condition is very useful in understanding the role of peristaltic muscular contraction in transporting biofluid behaving like a particle-fluid mixture. Also the theory is important to the engineering applications of pumping solid-fluid mixture by peristalsis.

In this research, the peristaltic flow with heat transfer through the two-dimensional horizontal tube of compliant wall properties with slip at boundaries is analyzed analytically. An approximated theoretical model is constructed of springbacked flexible compliant walls pipe, chosen to move as sinusoidal wave. Perturbation solution of the governing equations is obtained with small parameter ε, which means the amplitude ratio, and defined as the ratio of wave amplitude divided by tube radius. The influence of several parameters of slip conditions, wall properties and heat transfer on the dynamics of the liquid through the tube is mathematically studied, resulting in relations describing the fluid flow behavior and the induced net flow rate under the various values of flow parameters as "liquid compressibility, slip flow factor, and wave number", heat transfer parameter like Prandtl number, and elastic wall parameters such as "wall tension, wall damping coefficient, wall stiffness, and wall rigidity". Graphs for net flow rate under the effect of pervious parameters are plotted. Results disclose that the parameters of tube wall features, compressibility of liquid, Knudsen number for wall slip, and heat transfer in the presence of peristaltic pumping have a significant effect on net flow rate induced. This research has numerous related applications in different branches of science such as biological studies for blood flow motion in living creatures and also in industry including simulation of induced elastic waves for fluid flow through a tube.

Abstract-The I. INTRODUCTIONMHD viscous flow though pipes plays significant role in different areas of science and technology such as Petroleum industry, Biomechanics, Drainage and Irrigation engineering and so on. The investigations of blood flow through arteries are of considerable importance in many cardiovascular diseases particularly atherosclerosis. The pulsatile flow of blood through an artery has drawn the attention to the researchers for a long time due to its great importance in medical sciences. Under normal conditions, blood flow in the human circulatory system depends upon the pumping action of the heart and this produces a pressure gradient throughout the arterial network [1], [2]. During the last decades extensive research work has been done on the fluid dynamics of biological fluids in the presence of magnetic field. The flow of a conducting fluid in a circular pipe has been investigated by many authors [3]- [5]. References [6], [7] have studied steady viscous incompressible flow through  Manuscript