A Study of Nonlinear Variable Viscosity in Finite-Length Tube with Peristalsis

Peristaltic motion of an incompressible Newtonian fluid with variable viscosity induced by periodic sinusoidal traveling wave propagating along the walls of a finite-length tube has been investigated. A perturbation method of solution is sought. The viscosity parameter α (α << 1) is chosen as a perturbation parameter and the governing equations are developed up to the first-order in the viscosity parameter (α). The analytical solution has been derived for the radial velocity at the tube wall, the axial pressure gradient across the length of the tube, and the wall shear stress under the assumption of low Reynolds number and long wavelength approximation. The impacts of physical parameters such as the viscosity and the parameter determining the shape of the constriction on the pressure distribution and on the wall shear stress for integral and non-integral number of waves are illustrated. The main conclusion that can be drawn out of this study is that the peaks of pressure fluctuate with time and attain different values with non-integral numbers of peristaltic waves. The considered problem is very applicable in study of biological flow and industrial flow

Two layers of immiscible fluids in a vertical semi-corrugated channel with heat transfer: Impact of nanoparticles

Flow characteristics of two immiscible fluids in a vertical semi-corrugated channel with natural convection under the effect of the magnetic field are studied. The channel is divided into two regions the first one is filled with magneto nanofluid containing different types of nanoparticles such as Alumina (Al2O3), Copper (Cu), Copper oxide (CuO), Silver (Ag) and Titanium oxide (TiO2), and the other one is filled with a clear nonconducting viscous fluid. The linearization technique is used to solve the pertinent nonlinear equations governing the flow. An analysis for velocities, streamlines, and heat transfer has been introduced for various values of the problem parameters. A comparison between the zeroth-order analytical and numerical solutions for velocity, shear stress, and the temperature is also given. The results show that, the heat transfer enhancement increases with elevation of the nanoparticle volume fraction not only in the nanofluid layer but also in the clear fluid layer in the absence of the heat source. Keywords: Immiscible fluids, Nanofluid, Magnetic field, Heat transfe

Peristaltic Transport of a Particle–Fluid Suspension through a Uniform and Non-Uniform Annulus

This study looks at the influence of an endoscope on the peristaltic flow of a particle–fluid suspension (as blood model) through tubes. A long wavelength approximation through a uniform and non-uniform infinite annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically. The inner tube is uniform, rigid and moving with a constant velocity V0, whereas the outer non-uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase uf, particulate phase up and the pressure gradients have been obtained in terms of the dimensionless flow rate Q, the amplitude ratio ɸ, particle concentration C, the velocity constant V0 and the radius ratio ϵ (the ratio between the radius of the inner tube and the radius of the outer one at the inlet). Numerical calculations for various values of the physical parameters of interest are carried out for the pressure rise and the friction force on the inner and the outer tubes

The Influence of a Micropolar Fluid on Peristaltic Transport in an Annulus: Application of the Clot Model

A serious pathological condition is encountered when some blood constituents deposited on the blood vessels get detached from the wall, join the blood stream again and form a clot. Study of the peristaltic transport of a micropolar fluid in an annular region is investigated under low Reynolds number and long wavelength approximations. We model a small artery as a tube having a sinusoidal wave travelling down its wall and a clot model inside it. Closed form solutions are obtained for the velocity and the microrotation components, as well as the stream function, and they contain new additional parameters, namely, δ, the height of the clot, N, the coupling number and m, the micropolar parameter. The pressure rise and friction force on the inner and the outer tubes have been discussed for various values of the physical parameters of interest

Particulate suspension slip flow induced by peristaltic waves in a rectangular duct: Effect of lateral walls

This paper looks at the influence of lateral walls on peristaltic transport of a particle fluid suspension model applied in a non-uniform rectangular duct with slip boundaries. The peristaltic waves propagate on the horizontal sidewalls of a rectangular duct. The flow analysis has been developed for low Reynolds number and long wavelength approximation. Exact solutions have been established for the axial velocity and stream function. The effects of aspect the ratio β (ratio of height to width) and the volume fraction density of the particles C on the pumping characteristics are discussed in detail. The expressions for the pressure rise and friction forces on the wall of a rectangular duct were computed numerically and were plotted with variation of the flow rate for different values of the parameters. It is observed that in the peristaltic pumping (Δp>0,Q>0) and retrograde pumping (Δp>0,Q0) the behavior is quite opposite. Furthermore it is also observed that the pressure rise increases in the upper half of the channel and decreases in the lower half of the channel with the increase in lslip parameter. Keywords: Fluid suspension, Lateral walls, Peristaltic pumping, Partial sli