Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on Peristaltic Flow with Viscous Dissipation and Induced Magnetic Field

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic （MHD） fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.

Endoscopic Effects on Peristaltic Flow of a Nanofluid

In the present investigation we have studied the peristaltic flow of a nanofluid in an endoscope. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Analytical solutions have been calculated using Homotopy perturbation method （HPM） for temperature and nanoparticle equation while exact solutions have been calculated for velocity and pressure gradient. Numerical integration have been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated for five different peristaltic waves. Streamlines have been plotted at the end of the article.

Hybrid Effects of Thermal and Concentration Convection on Peristaltic Flow of Fourth Grade Nanofluids in an Inclined Tapered Channel: Applications of Double-Diffusivity

This article brings into focus the hybrid effects of thermal and concentration convection on peristaltic pumping of fourth grade nanofluids in an inclined tapered channel.First,the brief mathematical modelling of the fourth grade nanofluids is provided along with thermal and concentration convection.The Lubrication method is used to simplify the partial differential equations which are tremendously nonlinear.Further,analytical technique is applied to solve the differential equations that are strongly nonlinear in nature,and exact solutions of temperature,volume fraction of nanoparticles,and concentration are studied.Numerical and graphical findings manifest the influence of various physical flow-quantity parameters.It is observed that the nanoparticle fraction decreases because of the increasing values of Brownian motion parameter and Dufour parameter,whereas the behaviour of nanoparticle fraction is quite opposite for thermophoresis parameter.It is also noted that the temperature profile decreases with increasing Brownian motion parameter values and rises with Dufour parameter values.Moreover,the concentration profile ascends with increasing thermophoresis parameter and Soret parameter values.

Peristaltic flow in an asymmetric channel with convective boundary conditions and Joule heating

The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic(MHD) fluids are considered. Mathematical analysis has been presented in a wave frame of reference. The resulting problems are non-dimensionalized. Long wavelength and low Reynolds number approximations are employed. Joule heating effect on the thermal equation is retained. Analytic solutions for stream function and temperature are constructed. Numerical integration is carried out for pressure rise per wavelength. Effects of influential flow parameters have been pointed out through graphs.

Peristaltic flow of MHD Jeffrey fluid through finite length cylindrical tube

The present investigation studies the peristaltic flow of the Jeffrey fluid through a tube of finite length. The fluid is electrically conducting in the presence of an applied magnetic field. Analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. Expressions of the pressure gradient, volume flow rate, average volume flow rate, and local wall shear stress are obtained. The effects of relaxation time, retardation time, Hartman number on pressure, local wall shear stress, and mechanical efficiency of peristaltic pump are studied. The reflux phenomenon is also investigated. The case of propagation of a non-integral number of waves along the tube walls, which are inherent characteristics of finite length vessels, is also examined.

Peristaltic flow of Sisko fluid in a uniform inclined tube

We have analyzed an incompressible Sisko fluid through an axisymmetric uniform tube with a sinusoidal wave propagating down its walls. The present analysis of non- Newtonian fluid is investigated under the considerations of long wavelength and low Reynolds number approximation. The analytic solution is obtained using （i） the regular perturbation method （ii） the Homotopy analysis method （HAM）. The comparison of both the solutions is presented graphically. The results for the pressure rise, frictional force and pressure gradient have been calculated numerically and the results are studied for various values of the physical parameters of interest, such as α （angle of inclination）, b^＊ （Sisko fluid parameter）, Ф （amplitude ratio） and n （power law index）. Trapping phenomena is discussed at the end of the article.

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.

Peristaltic flow of Walter’s B fluid in endoscope

The peristaltic flow of a Walter＇s B fluid in an endoscope is studied. The problem is modeled in a cylindrical coordinate system. The main theme of the present analysis is to study the endoscopic effects on the peristaltic flow of the Waiter＇s B fluid. To the best of the authors＇ knowledge, no investigation has been made so far in the literatures to study the Walter＇s B fluid in an endoscope. Analytical solutions axe obtained using the regular perturbation method by taking 5 as a perturbation parameter. The approximate analytical solutions for the pressure rise and friction forces are evaluated using numerical integration. The effects of emerging parameters of the Waiter＇s B fluid are presented graphically.

Impact of Magnetic Field on a Peristaltic Flow with Heat Transfer of a Fractional Maxwell Fluid in a Tube

Magnetic field and the fractional Maxwell fluids’impacts on peristaltic flows within a circular cylinder tube with heat transfer was evaluated while assuming that they are preset with a low-Reynolds number and a long wavelength.Utilizing,the fractional calculus method,the problem was solved analytically.It was deduced for temperature,axial velocity,tangential stress,and heat transfer coefficient.Many emerging parameters and their effects on the aspects of the flow were illustrated,and the outcomes were expressed via graphs.A special focus was dedicated to some criteria,such as the wave amplitude’s effect,Hartman and Grashof numbers,radius and relaxation–retardation ratios,and heat source,which were under discussions on the axial velocity,tangential stress,heat transfer,and temperature coefficients across one wavelength.Multiple graphs of physical interest were provided.The outcomes state that the effect of the criteria mentioned beforehand(the Hartman and Grashof numbers,wave amplitude,radius ratio,heat source,and relaxation–retardation ratio)were quite evident.

Analysis of Combined Convective and Viscous Dissipation Effects for Peristaltic Flow of Rabinowitsch Fluid Model

In this article, mathematical modeling for peristaltic flow of Rabinowitsch fluid model is considered in a non-uniform tube with combined effects of viscous dissipation and convective boundary conditions. Wall properties analysis is also taken into account. Non-dimensional differential equations are simplified by using the well-known assumptions of low Reynolds number and long wavelength. The influence of various parameters connected with this flow problem such as rigidity parameter E1, stiffness parameter E2, viscous damping force parameter E3, Brickman number and Biot number are plotted for velocity distribution, temperature profile and for stream function. Results are plotted and discussed in detail for shear thinning, shear thickening and for viscous fluid. It is found that velocity profile is an increasing function of rigidity parameter, stiffness parameter, and viscous damping force parameter for shear thinning and for viscous fluid, due to the less resistance offered by the walls but, quite opposite behavior is depicted for shear thickening fluids. It is seen that Brickman number relates to the viscous dissipation effects, so it contributes in enhancing fluid temperature for all cases.

The Mathematical Analysis for Peristaltic Flow of Hyperbolic Tangent Fluid in a Curved Channel

In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation,long wave length and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method (HPM). The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise and stream functions.

Numerical Simulation of MHD Peristaltic Flow with Variable Electrical Conductivity and Joule Dissipation Using Generalized Differential Quadrature Method

In this paper, the MHD peristaltic flow inside wavy walls of an asymmetric channel is investigated, where the walls of the channel are moving with peristaltic wave velocity along the channel length. During this investigation,the electrical conductivity both in Lorentz force and Joule heating is taken to be temperature dependent. Also, the long wavelength and low Reynolds number assumptions are utilized to reduce the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. The new set of obtained equations is then numerically solved using the generalized differential quadrature method(GDQM). This is the first attempt to solve the nonlinear equations arising in the peristaltic flows using this method in combination with the Newton-Raphson technique. Moreover, in order to check the accuracy of the proposed numerical method, our results are compared with the results of built-in Mathematica command NDSolve. Taking Joule heating and viscous dissipation into account, the effects of various parameters appearing in the problem are used to discuss the fluid flow characteristics and heat transfer in the electrically conducting fluids graphically. In presence of variable electrical conductivity, velocity and temperature profiles are highly decreasing in nature when the intensity of the electrical conductivity parameter is strengthened.

Series solution of unsteady peristaltic flow of a Carreau fluid in small intestines

The study of peristaltic flow of a Carreau fluid in a non-uniform tube under the con- sideration of long wavelength is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave e. Numerical integration has been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated through graphs.

Effects of the wall properties on unsteady peristaltic flow of an Eyring-Powell fluid in a three-dimensional rectangular duct

In the present investigation, peristaltic flow Powell） has been taken into consideration in of non-Newtonian fluid model （Eyring- a cross-section of three-dimensional rect- angular channel. The flow is taken to be unsteady and incompressible. The observations are made under the limitations of low Reynolds number and long wavelength which helps in reducing the governing equations. The walls of the channel are supposed to be compliant. The obtained equations are nonlinear partial differential equation of second order and have been solved analytically by using series solution technique. The achieved results are then portrayed graphically to see the variation of various emerging parame- ters on the profile of velocity. The stream functions have also been sketched in order to discuss the trapping behavior of the circular bolus.

Mathematical study for peristaltic flow of Williamson fluid in a curved channel

In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equa- tions are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.

Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls.Mathematical modeling is based upon the laws of mass and linear momentum.Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations.The features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of interest.Trapping bolus scheme is also presented through streamlines.

Numerical Study of Mixed Convective Peristaltic Flow through Vertical Tube with Heat Generation for Moderate Reynolds and Wave Numbers

The current study focuses on the numerical investigation of the mixed convective peristaltic mechanism through a vertical tube for non-zero Reynolds and wave number. In the set of constitutional equations, energy equation contains the term representing heat generation parameter. The problem is formulated by dropping the assumption of lubrication theory that turns the model mathematically into a system of the nonlinear partial differential equations. The results of the long wavelength in a creeping flow are deduced from the present analysis. Thus, the current study explores the neglected features of peristaltic heat flow in the mixed convective model by considering moderate values of Reynolds and wave numbers. The finite element based on Galerkin's weighted residual scheme is applied to solve the governing equations. The computed solution is presented in the form of contours of streamlines and isothermal lines, velocity and temperature profiles for variation of different involved parameters. The investigation shows that the strength of circulation for stream function increases by increasing the wave number and Reynolds number. Symmetric isotherms are reported for small values of time-mean flow. Linear behavior of pressure is noticed by vanishing inertial forces while the increase in pressure is observed by amplifying the Reynolds number.

Exact solution to peristaltic transport of power-law fluid in asymmetric channel with compliant walls

Effects of compliant wall properties on the peristaltic flow of a non-Newtonian fluid in an asymmetric channel are investigated.The rheological characteristics are characterized by the constitutive equations of a power-law fluid.Long wavelength and low Reynolds number approximations are adopted in the presentation of mathematical developments.Exact solutions are established for the stream function and velocity.The streamlines pattern and trapping are given due attention.Salient features of the key parameters entering into the present flow are displayed and important conclusions are pointed out.

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.