Analysis of Exponentially Increasing Dependent Wave Amplitude of Peristaltic Pumping of Casson Fluid through Channels

The experimentally verified fact that there is a high pressure zone in the lower part of the oesophagus has established that the earlier models fall short of representing the realistic swallowing process in the oesophagus. Since the high pressure is created by gradually increasing amplitudes of peristaltic waves, swallowing of Casson fluid in oesophagus is mathematically remodeled. It is revealed that in the case of exponentially increasing amplitude, pressure is non-uniformly distributed for different cycles. Pressure increases along the entire length of the oesophagus; and finally toward the end of the oesophageal flow, it increases quite significantly, probably to ensure delivery into the stomach. This is a similar observation for Newtonian as well as non-Newtonian fluids but Casson fluids need more pressure; and hence more efforts are required by the oesophagus to transport the fluid forward. When wave amplitude is small, flow rates are small. In such a case, Casson fluid requires higher flow rates for reflux to occur in comparison to Newtonian fluid. This tendency gradually diminishes with increasing amplitude. For a particular value of amplitude, there is no difference; and beyond that the trends are quite opposite. Thus, Casson fluid is found to be less prone to reflux near the wall. It is also concluded that for the Newtonian fluid as well as for the non-Newtonian Casson fluid, reflux is more likely to occur with increasing amplitude and it is further augmented by the addition of amplifying parameter.

A theoretical investigation is performed for free convective peristaltic pumping of a Casson fluid through an inclined porous wavy channel. The flow is subjected to uniform magnetic field in the transverse direction. In addition, the energy equation contains porous and viscous dissipation effects. The governing flow problem is modeled for Casson fluid with the help of conservation laws of mass, momentum, and energy under the long wavelength assumption. Using a regular perturbation method, we obtained the analytical expressions for the axial velocity, temperature, pressure rise per one wavelength, and heat transfer rate. The consequences of various effects on the flow quantities are demonstrated in the form of graphical representations and discussed in detail. The findings reveal that the rise in the thermal Grashof number and permeability parameter leads to an increment in the velocity and thermal fields. The heat transfer rate strengthened when the Casson parameter and magnetic parameter were increased. The pressure rise exhibits an enhancing trend for the Brinkmann number and permeability parameter. Further, we observed a decreasing behavior on streamlines for increasing magnetic field strength. Moreover, the obtained findings are applicable to a variety of fields in the bioengineering and medical sciences, such as targeted drug delivery, heart-lung machines, MRI, cancer therapy, power conversion devices, and micromanufacturing processes.

The effect of peristalsis on dispersion in Casson fluid flow

PurposeOhmic heating generates temperature with the help of electrical current and resists the flow of electricity. Also, it generates heat rapidly and uniformly in the liquid matrix. Electrically conducting biofluid flows with Ohmic heating have many biomedical and industrial applications. The purpose of this study is to provide the significance of the effects of Ohmic heating and viscous dissipation on electrically conducting Casson nanofluid flow driven by peristaltic pumping through a vertical porous channel.Design/methodology/approachIn this analysis, the non-Newtonian properties of fluid will be characterized by the Casson fluid model. The long wavelength approach reduces the complexity of the governing system of coupled partial differential equations with non-linear components. Using a regular perturbation approach, the solutions for the flow quantities are established. The fascinating and essential characteristics of flow parameters such as the thermal Grashof number, nanoparticle Grashof number, magnetic parameter, Brinkmann number, permeability parameter, Reynolds number, Casson fluid parameter, thermophoresis parameter and Brownian movement parameter on the convective peristaltic pumping are presented and thoroughly addressed. Furthermore, the phenomenon of trapping is illustrated visually.FindingsThe findings indicate that intensifying the permeability and Casson fluid parameters boosts the temperature distribution. It is observed that the velocity profile is elevated by enhancing the thermal Grashof number and perturbation parameter, whereas it reduces as a function of the magnetic parameter and Reynolds number. Moreover, trapped bolus size upsurges for greater values of nanoparticle Grashof number and magnetic parameter.Originality/valueThere are some interesting studies in the literature to explain the nature of the peristaltic flow of non-Newtonian nanofluids under various assumptions. It is observed that there is no study in the literature as investigated in this paper.

The paper is concerned with the peristaltic-ciliary transport of a viscoplastic fluid (Casson fluid) through an inclined cylindrical tube. The peristalsis-cilia induced motion is analysed in the moving frame of reference under the lubrication approximations. Solutions to the flow characteristics petering to yielded and unyielded regions are obtained. The effects of various physical parameters on the axial velocity, the pumping characteristics, the pressure rise, and the frictional force over one wavelength, along with the trapping phenomenon are presented through graphs. Further, the peristaltic flow and peristaltic-ciliary flow results are compared. It is noticed that the axial velocity and the size of trapping bolus in the unplug flow region decrease with an increase in the yield stress. In addition, the axial velocity and the axial pressure gradient in the peristaltic-ciliary pumping are higher than those in the peristaltic pumping.

This paper is concerned with the peristaltic transport of an incompressible non-Newtonian fluid in an elastic tube. Here the flow is due to three different peristaltic waves and two different types of elastic tube. The constitution of blood suggests a non-Newtonian fluid model and it demands the applicability of yield stress fluid model. Among the available yield stress fluid models for blood, the non-Newtonian Casson fluid is preferred. The Casson fluid model describes the flow characteristics of blood accurately at low shear rates and when it flows through small blood vessels. Long wavelength approximation is used to linearize the governing equations. The effect of peristalsis and non-Newtonian nature of blood on velocity, plug flow velocity, wall shear stress and the flux flow rate are derived. The flux is determined as a function of inlet, outlet, external pressures, yield stress, amplitude ratio, and the elastic properties of the tube. Furthermore, it is observed that, the yield stress, peristaltic wave, and the elastic parameters have strong effects on the flux of the non-Newtonian fluid, namely, blood. One of the important observation is that the flux is more when the tension relation is an exponential curve rather than that of a fifth degree polynomial. Further, in the absence of peristalsis and when the yield stress tends to zero our results agree with the results of Rubinow and Keller (1972). This study has significance in understanding peristaltic transport of blood in small blood vessels of living organisms.

Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid.

The influence of ultrasonic radiation on the flow of a liquid through a porous medium is analyzed. The analysis is based on a mechanism proposed by Ganiev et al. according to which ultrasonic radiation deforms the walls of the pores in the shape of travelling transversal waves. Like in peristaltic pumping, the travelling transversal wave induces a net flow of the liquid inside the pore. In this article, the wave amplitude is related to the power output of an acoustic source, while the wave speed is expressed in terms of the shear modulus of the porous medium. The viscosity as well as the compressibility of the liquid are taken into account. The Navier–Stokes equations for an axisymmetric cylindrical pore are solved by means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the pore is the small parameter. In the second-order approximation a net flow induced by the travelling wave is found. For various values of the compressibility of the liquid, the Reynolds number and the frequency of the wave, the net flow rate is calculated. The calculations disclose that the compressibility of the liquid has a strong influence on the net flow induced. Furthermore, by a comparison with the flow induced by the pressure gradient in an oil reservoir, the net flow induced by a travelling wave can not be neglected, although it is a second-order effect.

Peristaltic pumping by a sinusoidal travelling wave in the walls of a two-dimensional channel filled with a viscous incompressible couple-stress fluid, is investigated theoretically. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio (wave amplitude:channel half width) is small. The results show that the mean axial velocity decreases with increasing couple-stress parameter eta . The phenomenon of reflux (mean flow reversal) is discussed. A reversal of velocity in the neighbourhood of the centre line occurs when the pressure gradient is greater than that of the critical reflux condition. It is found that the critical reflux pressure increases with the couple-stress parameter. Numerical results are reported for various values of the physical parameters of interest.

The axisymmetric peristaltic flow of a viscous compressible liquid through the gab between two coaxial tubes (annulus) was studied. This peristaltic flow is actually a result of the influence of ultrasonic radiation on the flow of a liquid through an annulus, which deforms the walls of the outer tube in the shape of traveling transversal waves exactly like peristaltic pumping. Those traveling transversal waves induce a net flow of the liquid inside the annulus. This problem has numerous applications in various branches of science, including stimulation of fluid flow in the annulus under the effect of elastic waves and studies of blood flow dynamics in living creatures. The wave amplitude is related to the power output of an acoustic source. A perturbation technique was employed to analyze the problem where the amplitude ratio (wave amplitude/outer tube radius at inlet) is chosen as a parameter. In the second-order approximation, a net flow induced by the traveling wave was calculated for various v...

Peristaltic transport of a compressible viscous liquid through a tapered pore

Peristaltic pumping is a process of fluid transport arising from the progressive waves, which travel along the walls of a flexible channel. It is a primary physiological transport mechanism that is inherent in many tubular organs of the human body such as the ureter, the gastro-intestinal tract, the urethra, and so on. Many studies exist in literature with the aim of understanding the characteristics of peristaltic flow under the assumption of low Reynolds number and infinitely long wavelength in a two-dimensional channel. However, peristaltic pumping is also the mechanism used in other industrial applications such as the blood pump for which the Reynolds number has a moderately high value. As studies concerning moderate to high Reynolds number flow in the circular tube are rare in literature, in the present study, the peristaltic flow of an incompressible fluid is numerically simulated using the finite volume method for solving the incompressible Navier-Stokes equations in primitive variable formulation by means of an infinite train of sinusoidal waves traveling along the wall of an axi-symmetric tube. The computational model presented in this work covers a wider range of Reynolds number (0.01-100), wave amplitude (0-0.8), and wavelength (0.01-0.4) than the those attempted in previous studies reported in literature and some new results pertaining to the distribution of velocity, pressure, wall shear stress for different peristaltic flow conditions characterizing flow at moderately higher Reynolds number have been obtained. The effect of the wave amplitude, wavelength, and Reynolds number on the "flow trapping" mechanism induced by peristalsis has also been investigated here for higher ranges of values of the parameters characterizing peristalsis.

Decreased pulsatile blood flow may occur in certain clinical conditions in which congenital or acquired constriction is present in a major artery. Coarctation of the aorta, renal arterial stenosis, and arteriosclerotic narrowing of visceral and peripheral arteries may produce significant dampening of the pulse wave distal to the site of partial obstruction. Diminished pulsatile blood flow is also present during open heart surgery when roller pumps are used in the extracorporeal circuit. The optimum form and amplitude of the pulse wave is important in the development of prosthetic indwelling mechanical hearts. These considerations prompted us to study the vascular response to pulsatile and nonpulsatile blood flow. The resistance of the systemic and pulmonary arterial beds to each type of perfusion was investigated in dogs. <h3>Methods</h3><h3>Group A.—</h3> A left thoracotomy and total cardiopulmonary bypass were performed upon 40 dogs anesthetized with 5% thiopental sodium (Fig 1). Adequate ventilation with oxygen

Effects of an endoscope and fluid with variable viscosity on peristaltic motion

Electroosmotically assisted peristaltic propulsion of blood-based hybrid nanofluid through an endoscope with activation energy