Peristaltic Flow Research Articles

The effect of peristalsis on dispersion in Casson fluid flow

The present study examines the peristaltic flow of a non-Newtonian (Casson) fluid and solute transport through a flexible tube. Using the long-wavelength approximation, an analytical solution for the Casson fluid velocity is obtained in the axial and radial directions. Then, a numerical solution to the solute concentration is computed using the standard Galerkin finite element method (FEM) for the case of solutal convection-diffusion and the Discontinuous Galerkin FEM for the pure convection case. Graphical results are presented for the axial and local solute concentrations, and the influence of peristaltic wave amplitude, volumetric flow rate, modified Péclet number, time, yield stress, and pertinent initial condition parameters were investigated.

Numerical treatment of entropy generation and Bejan number into an electroosmotically-driven flow of Sutterby nanofluid in an asymmetric microchannel

This article aims to investigate the electrokinetic peristaltic flow of the Sutterby nanofluid through an asymmetric microchannel with a porous medium and the Joule heating parameter. The magnetic field is applied in the transverse direction and the electric field on the flow direction. The flow model consists of the continuity, momentum, heat, and electric potential equations, with appropriate boundary conditions. The Debye-Hückel linearization approximation is considered. Under the long wavelength and small Reynolds number approximation, the lengthy equations were reduced. The resultant coupled equations are numerically solved by the renowned NDSolve coding using Mathematica software. Entropy and Bejan number are also incorporated in this study. The velocity, temperature, and the phenomenon of entrapment are analyzed in depth with the aid of graphical representations. Streamlines of various waveforms are also discussed. The analysis discovered that the velocity of the fluid enhanced for porosity parameter and reverse effects is observed on the quantity of the magnetic parameter.

Thermal and mass exchange in a multiphase peristaltic flow with electric-debye-layer effects and chemical reactions using machine learning

The present investigation delves into the analysis of mass and thermal transmission during the peristalsis of a two phase flow of a Prandtl fluid, within a symmetric channel by considering entropy generation and minimization. The considered flow is examined by taking into account the impacts of electroosmotic effects through Electric Debye Layer (EDL) and chemical reactions followed by the lubrication theory approximation. Numerical solutions are acquired for the consequential differential equations through artificial neural networks (ANN) based fitness functions. The artificial neural networks (ANN) based fitness function optimized through hybrid evolutionary algorithms especially ABC (artificial bee colony) and NNA (neural network algorithm) like ANN-ABC-NNA. For the efficiency and validation of the algorithm we conduct the one hundred (100) independent runs. The obtained results through ANN-ABC-NNA are compared with the exact solutions for validation of results. In the present examination, the velocity profile is noticed to increase by the rise in the electroosmotic factor and solid particles concentration, while it decreases for the Prandtl fluid parameter. This research holds practical significance in diverse applications, particularly in the design and optimization of microfluidic devices.

Viscous Dissipation and Mixed Convection Effects on the Induced Magnetic Field for Peristaltic Flow of a Jeffrey Nanofluid

The issue of Jeffrey nanofluid peristaltic flow in an asymmetric channel being affected by an induced magnetic field was studied. In addition, mixed convection and viscous dissipation were considered. Under the supposition of a long wave length and a low Reynolds number, the problem was made simpler. The system and corresponding boundary conditions were solved numerically by using the built-in package NDSolve in Mathematica software. This software ensures that the boundary value problem solution is accurate when the step size is set appropriately. It computes internally using the shooting method. Axial velocity, temperature distribution, nanoparticle concentration, axial induced magnetic field, and density distribution were all calculated numerically. An analysis was conducted using graphics to show how different factors affect the flow quantities of interest. The results showed that when the Jeffrey fluid parameter is increased, the magnitude of axial velocity increases at the upper wall of the channel, while it decreases close to the lower walls. Increasing the Hartmann number lads to increases in the axial velocity near the channel walls and in the concentration of nanoparticles. Additionally, as the Brownian motion parameter is increased, both temperature and nanoparticle concentration grow.

Complex cilia-generated flow of hybrid nanofluid with electroosmosis, viscous dissipation and slippage

In this study, we investigated how electroosmsis, viscous dissipation, and slippage affect the peristaltic flow of complex cilia-generated flow of hybrid nanofluid in a ciliated tube. The complex cilia-generated flow is characterized by a complex sinusoidal wave that transmits along the wall of the tube with a uniform speed having distinct amplitudes. The main objective of this work is to examine how this complex cilia on the wall drives the hybrid nanofluid flow under electroosmosis. The Helmholtz–Smoluchowski equation is used to model the electroosmosis, and the Poisson equation is solved analytically using the Debye-Huckel approximation. The lubrication approach is utilized to simplify the governing equations. The governing non-dimensional equations for hybrid nanofluid are solved exactly using the DSolve command of Mathematica. The results are presented graphically to accomplish the theoretical results from the complex-cilia wave evolution from the necessary flow parameters in an asymmetric tube. The study shows that increasing the electroosmotic parameter leads to an increase in the velocity profile at the boundary and a decrease in the middle of the tube. Conversely, the Helmholtz–Smoluchowski velocity parameter has the opposite effect. The Brinkman parameter increases the temperature of the hybrid nanofluid. The study also presents a graphical analysis of pressure rise and pressure gradient for various values of the parameters. The pressure rise against volumetric flow is rate and pressure gradient increases by increasing the electroosmotic parameter and Helmholtz-Smoluchowski parameter, while it decreases for increasing the velocity slip parameter. The streamlines are drawn to study the trapping phenomena of blood in the hybrid nanofluid flow in an asymmetric tube by the formation of bolus and the division of streamlines. It is observed that the size and number of bolus close to the artery walls increases for electroosmotic parameter while reverse behavior is observed for Helmholtz-Smoluchowski parameter. The tabular presentation of the heat transfer coefficient at the wall is presented. The current results can be used in bio mathematical models to control fluid flow through micro-channels and to investigate ways to cure artery blockages and cancer tumors in biomedicine. The study can also be used to design and optimize microfluidic devices for drug delivery, lab-on-a-chip devices, and other biomedical applications.

Electro-osmotic peristaltic flow of non-Newtonian Sutterby TiO2 nanofluid inside a microchannel through porous medium with modified Darcy’s law

The primary aim of this study was to examine the peristaltic flow of an unsteady non-Newtonian TiO2 nanofluid through a uniformly symmetric channel under the influence of electro-osmosis. The fluid behavior was modeled by the Sutterby model. Furthermore, the flow took place through a porous medium, following a modified form of Darcy’s law. Additionally, the impacts of Dufour and Soret effects, chemical reaction, activation energy, viscous dissipation, heat generation, and thermal radiation were considered. A wave transformation was used to simplify the governing equations describing the velocity, temperature, and nanoparticle concentration. These simplified equations were then solved analytically using the homotopy perturbation method. Additionally, set figures were employed to illustrate and discuss the impact of the physical parameters involved in the problem on the obtained solutions. It is found that the presence of a modified Darcy’s medium in the Navier–Stokes equation results in a porous term that is dependent on the index of the Sutterby model. Furthermore, it is found that as the thermophoresis parameter increases, the nanoparticles are more concentrated, and their flow from the hot region to the cold region is more effective. Additionally, it is observed that in the presence of thermal radiation, the activation energy and the Brownian motion parameter have similar effects on the concentration profile.

Peristalsis of Fractional Second Grade Fluid in the Presence of Electro Osmotic Phenomenon with Heat and Mass Transfer

MRI method is used in magnetic resonance imaging (MRI) to diagnose brain disorders by detecting the changing conditions within the brain. Peristaltic waves created on the flexible walls of the brain cause particles to move, and understanding this fluid flow can benefit the treatment of malignant tissues. In light of this, the electro-osmotic impact on the peristaltic flow of a fractional second grade fluid (ionic solution) in a microchannel with a heat and mass transfer is investigated. The governing equations of the modulated problem can be solved analytically by assuming a low Reynolds number (Re → 0) and a long wavelength (δ << 1). An analysis of the Poisson-Boltzmann equation is considered to examine the electro-kinetic mechanism. Using the Mathematica program, we solved a set of dimensionless equations and displayed the generated graphs. We analyzed relevant factors for their impacts on temperature, velocity, and pressure gradient. Biomedical engineers may find inspiration to create bio-microfluidic devices that aid in the movement of physiological fluids based on the model and its related findings.

An analytical and comparative study of swallowing in a tumor-infected oesophagus: a mathematical model.

This study discusses non-steady effects encountered in peristaltic flows in oesophagus. The purpose of this communication is to evolve a mechanism to diagnose tumor in an oesophagus mathematically. The tumor is modelled by generic bump function of certain height and width. The method of solution follows long wavelength and low-Reynolds number approximations for unsteady flow, while integrations have been performed numerically in order to plot graphs, which reveal various characteristics of the flow. The goal is to assess how pressure varies across the tumor's width. The spatial, as well as temporal, dependence of pressure has been studied in the laboratory frame of reference. The pressure distribution for tumor-infected oesophagus is compared with that of normal oesophagus. An intensified pressure is obtained in the presence of tumor. The interruption while swallowing through benign oesophageal tumor is confirmed by an abrupt pressure rise across the tumor's width. Tumor position also plays a significant role whether it is at contraction or relaxation of walls. Additionally, wall-shear-stress, volumetric flow rate and streamlines have also been described and compared with that without tumor growth. The expressions corresponding to all the physical quantities are computed numerically. Further, this model may also be implemented to the two-dimensional channel flow for an industrial application.

Effects of Rotation and Inclined Magnetic Field on Walters' B Fluid in a Porous Medium using perturbation method or technique.

The peristaltic flow of Walter's B fluid through an asymmetric channel is analyzed. The constitutive equation for the balance of mass, momentum, trapped phenomena, and velocity distribution is modeled. Consideration of low Reynolds number and long wavelength assumption are used in the flow analysis to get an exact solution by using the perturbation method. The impact of impotent parameters on stream function and axial velocity has been gained. The set of figures is graphically analyzed of these parameters.

The profound effect of heat transfer on magnetic peristaltic flow of a couple stress fluid in an inclined annular tube

In this study, we explore the analysis of peristaltic flow with heat transfer occurring within the gap between coaxial inclined tubes. The inner tube’s wall is rigid, while the outer tube’s wall features a sinusoidal wave propagating through it. The cylindrical system is employed to formulate the problem. The flow is characterized using continuity, momentum, and energy equations. We apply the assumption of long wavelength and the low Reynolds number approximation to simplify the nonlinear governing equation, subsequently solving it through perturbation techniques. We investigate the impact of crucial parameters, such as the magnetic field, porous media, slipping conditions, and others, on the peristaltic flow of a couple stress fluid. Our focus lies on assessing their influence on axial velocity, pressure gradient, and flow streamlines. The outcomes are visually presented through graphical representations. Notably, an increase in the slipping parameter results in a reduction of fluid velocity, attributed to the reverse slipping of the flow. The introduction of a magnetic field leads to an augmentation of the pressure gradient. Moreover, elevating the peristaltic amplitude and heat source induces the formation of a vortex within the flow. The presence of porous media leads to an increase in the pressure difference of the fluid flow. The primary objective of this research is to enhance our understanding of the peristaltic motion of non-Newtonian fluid dynamics, specifically incorporating a couple stress fluid. This contributes to a deeper understanding of crucial fluids, such as blood, within the human circulatory system. The implications extend to biological and industrial applications like magnetic resonance imaging (MRI) and radiosurgery, advancing our scholarly understanding of fluid behavior, especially in non-Newtonian scenarios.

Influence of inclined magnetic field and heat transfer on the peristaltic flow of Rabinowitsch fluid model in an inclined channel

The recent study is focused on discussion of heat transfer and magnetic field results of peristaltic flow of Rabinowitsch fluid model in an Inclined Channel. In this piece of research, peristalsis’s fundamental problem with heat transfer in the presence of a magnetic field is checked. An incompressible Rabinowitsch fluid is present in an inclined channel, which is considered as the reference for this research. The solutions are devised with the assumptions of long wavelength and low Reynolds number approximations. The resulting equations are then solved exactly by implementing various command of MATHEMATICA subject to relevant boundary conditions. Results are discussed for various flow quantities like temperature, velocity, tangential stress, pressure gradient and rise, and friction force. Computational simulations are performed to determine the flow quantities. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into flow quantities. Furthermore, this investigates how magnetic field and heat transfer parameters influence these peristaltic flow phenomena. The outcomes of important parameters were plotted and scrutinized. There is amultitude of medical implementations derived from the current consideration, such as the depiction of the gastric juice motion in the small intestine when an endoscope is inserted through it.

Catalytic effects on peristaltic flow of Jeffrey fluid through a flexible porous duct under oblique magnetic field: Application in biomimetic pumps for hazardous materials

Homogenous and heterogeneous reactions play an essential role in polymer production, combustion, ceramic production, catalysis, distillation, and biochemical procedures. As a result of this advancement, a mathematical model is developed to examine the role of catalytic chemical reaction effects on the magneto-hydrodynamic peristaltic transport in a flexible divergent duct containing a non-deformable porous medium as a model for complex hazardous waste bio-inspired pumping mechanisms. The Jeffrey model is utilized to simulate strong non-Newtonian characteristics. Additional multi-physical features included in the model are heat generation, thermal radiation, Hall current, and complaint wall properties along with an inclined (oblique) magnetic field. The long wavelength and low Reynolds number approximations are deployed to transform the primitive conservation equations from a moving boundary problem to a fixed frame. Appropriate transformations are then utilized to render the model dimensionless. The exact solutions are obtained for stream function and velocity. Further, the R-K-Fehlberg integration scheme is applied to solve the energy and concentration equations. Velocity, temperature, concentration, skin friction, and Nusselt number profiles are visualized graphically. Streamline patterns are also included to capture bolus dynamics. Validation with previous simpler studies has been included. A detailed appraisal of key control parameters on transport characteristics is conducted. It is found that velocity is suppressed with elevation in the damping force parameter while it is enhanced with an increment in regime permeability i. e. Darcy number. Both homogeneous and heterogeneous reactions are observed to exert a significant impact on the species concentration. The volume of the trapped fluid bolus size is shown to be an increasing function of the peristaltic wave amplitude ratio. The present work generalizes existing studies to consider catalytic effects on dissipative peristaltic pumping of the Jeffrey fluid with heat generation and radiative flux, aspects which have been neglected in a single model previously. The simulations are relevant to better characterize the complex transport phenomena in nuclear reactor waste transport via biologically inspired pumping designs.

Thermal storage study and enhancement of heat transfer through hybrid Jeffrey nanofluid flow in ducts under peristaltic motion with entropy generation

This article examines the analysis of peristaltic transport within a vertical sinusoidal wavy duct using a hybrid nanofluid composed of deionized blood and nanoparticles such as Graphene Oxide (Go) and Molybdenum disulfide (MoS2). The study also investigates volumetric entropy generation, employing the Jeffrey fluid model known for its representation of both viscous and elastic fluid behaviors. The mathematical framework integrates Navier–Stokes equations and the energy equation. Simplifying the analysis, non-dimensional equations are derived for the hybrid nanofluid in a two-dimensional coordinate system, assuming a long wavelength (δ < 1) and low Reynolds number (Re). The Galerkin finite element method via MATLAB is employed for numerical solutions. The results, depicted graphically using MATLAB, offer insights into temperature variations and the two-dimensional peristaltic flow concerning different parameters. To the best of authors knowledge entropy generation analysis is still not carried out for blood base Go-MoS2 hybrid nanofluid in a vertical wavy channel. The aim of the present study is to explore the contribution of significant parameters on entropy generation. One of the key findings includes that flow rate and Brinkmann number contribute to enhance entropy generation in presence of hybrid nanofluid.

Peristaltic transport of nanofluid with temperature dependent thermal conductivity: A numerical study

Peristaltic flow of nanofluid with temperature-dependent thermal conductivity is investigated. Variation of effective thermal conductivity of nanofluids with temperature is addressed. Mathematical modeling of momentum and energy equation is considered in a symmetric channel. Viscous dissipation, Ohmic heating, and mixed convection are accounted. Applied magnetic field and convective boundary conditions are imposed. Dimensionless expressions are simplified under long wavelength approximation. The relevant problems are solved by numerical technique. Velocity, temperature, pressure, and heat transfer characteristics are studied graphically. Heat transfer rate rapidly increases by increasing the concentration of nanomaterial. Therefore, nanomaterial is used for the cooling process in engineering and biomedical devices.

Hydromagnetic peristaltic flow of convective Casson nanofluid through a vertical porous channel under the influence of Ohmic heating and viscous dissipation effects

Purpose Ohmic 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/approach In 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. Findings The 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/value There 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.

Influence of Suction and Injection on Peristaltic Mechanism of a Jeffrey Nanofluid in a Vertical Channel with Complete Slip Effects

The main goal of the current study is to understand how the peristaltic system of a Jeffrey nanofluid operating in a vertical tube with complete slip properties is influenced by suction and injection. The peristaltic flow was examined by several researchers using various biological fluid types. The majority of the authors used viscous (Newtonian) fluids to illustrate the peristaltic flow mechanism. Because of its uses in industry, non-Newtonian fluids have attracted a great deal of attention. There are numerous models for non-Newtonian liquids because of the complexity of fluids. The Jeffrey fluid model is the most straightforward linear model to depict the non-Newtonian fluid characteristics for which it is reasonable to expect that accurate or analytical solutions would eventually be discovered. Nanofluids are innovative substances that have endless applications in engineering, biology, medicine and other fields. This mathematical model can be used effectively to transport cervical cancer in the tiny blood channels of the cervix. The resulting flow model is then effectively simulated with the appropriate assumptions of a small Reynolds number and long wavelength. The governing conservation equations are then established. Analytical solutions have been found for, pressure rates per wavelength, temperature, velocity and concentrations of nanoparticles in the resultant flow problem. Using the software WOLFRAM MATHEMATICA, the effects of all physical parameters on streamline, velocity, temperature, concentration fields, pressure gradient, frictional force and pressure rate are graphically analyzed. We observed in both 2D-plot and 3D-plot that we increasing the slip parameters β1 and β2 lead to increase the velocity profile. By raising the Jeffrey nanofluid parameter, the pressure rise is decreased. With frictional force, the opposite behavior is observed. The effect of suction and injection parameter k on the trapping bolus, which gets greater as k is higher.

Impact of Porous Media on Peristaltic Transport of Tangent Hyperbolic Nanofluid in Asymmetric Channel

The purpose behind this paper is to discuss nanoparticles effect, porous media, radiation and heat source/sink parameter on hyperbolic tangent nanofluid of peristaltic flow in a channel type that is asymmetric. Under a long wavelength and the approaches of low Reynolds number, the governing nanofluid equations are first formulated and then simplified. Associated nonlinear differential equations will be obtained after making these approximations. Then the concentration of nanoparticle exact solution, temperature distribution, stream function, and pressure gradient will be calculated. Eventually, the obtained results will be illustrated graphically via MATHEMATICA software.

Analytical investigation of Carreau fluid flow through a non-circular conduit with wavy wall

Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions. The mathematical equations are solved in their dimensionless form under the approximation of long wavelength. The solution of the momentum equation is obtained by applying perturbation technique (We2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_e^2$$\\end{document} as perturbation parameter) along with a polynomial solution. We introduce a new polynomial of twenty degrees to solve the energy equation. The solutions of mathematical equations are investigated deeply through graphical analysis. It is noted that non-Newtonian effects are dominant along the minor axis. It is found that flow velocity is higher in the channels having a high elliptical cross-section. It is observed from the streamlines that the flow is smooth in the mid-region, but they transform into contours towards the peristaltic moving wall of the elliptic duct.

Mathematical modeling of blood flow in an annulus porous region between two coaxial deformable tubes: An advancement to peristaltic endoscope

In the present work, the electromagnetohydrodynamic peristaltic flow of blood through an annulus region between two concentric circular tubes has been investigated for the advancement of a peristaltic endoscope. In this model, the viscous and incompressible blood is assumed as non-Newtonian Jeffery fluid, and tubes are inclined at an angle β with the horizontal. The governing equations for the considered problem are simplified under the assumption of a low Reynolds number and long wavelength approximations. An analytical expression for various flow variables such as axial velocity, radial velocity, time mean flow rate, volumetric flow rate, frictional force at the surface of the inner tube, and mechanical efficiency is obtained. In this work, we discussed the impact of various flow parameters like the Hartmann number M, electric field strength parameter H, Jeffery fluid parameter λ1, radius ratio n, occlusion ϕ=ba, angle of inclination β, and Darcy number Da on the above flow variables. The streamlines are also made to discuss the trapping phenomena of a fluid bolus inside the tubes. The comparison of pressure rise for the various endoscopes and the validation of the present result with the previously established results are discussed.

Microbic flow analysis of nano fluid with chemical reaction in microchannel with flexural walls under the effects of thermophoretic diffusion

The current investigation examines the peristaltic flow, in curved conduit, having complaint boundaries for nanofluid. The effects of curvature are taken into account when developing the governing equations for the nano fluid model for curved channels. Nonlinear & coupled differential equations are then simplified by incorporating the long wavelength assumption along with smaller Reynolds number. The homotopy perturbation approach is used to analytically solve the reduced coupled differential equations. The entropy generation can be estimated through examining the contributions of heat and fluid viscosities. The results of velocity, temperature, concentration, entropy number, and stream functions have been plotted graphically in order to discuss the physical attributes of the essential quantities. Increase in fluid velocity within the curved conduit is noticed for higher values of thermophoresis parameter and Brownian motion parameter further entropy generation number is boosted by increasing values of Grashof number.