Assumption Of Long Wavelength Research Articles

Radially varying magnetic field effect on peristaltic motion with heat and mass transfer of a non-Newtonian fluid between two co-axial tubes

The present analysis discusses the effects of thermal-diffusion with thermal radiation, Joule heating and internal heat generation on peristaltic flow of a non-Newtonian fluid obeying Jeffery model. Heat and mass transfer are also taken into consideration, the flow is between two co-axial tubes under the effect of radially varying magnetic field. The inner tube is uniform and at rest, while the outer tube is flexible with sinusoidal wave traveling. The problem is modulated mathematically by a system of partial differential equations which describes the equations of momentum, heat, and mass transfer. These equations are solved analytically under the assumptions of long wave length and low-Reynolds number in non-dimensional form. The solutions are obtained as a functions of physical parameters of the problem. The radially varying magnetic field effect on the temperature and concentration distributions is analyzed and it is shown that the increase of Hartman number tends to reduce the temperature, while it increases the concentration.

Heat and mass transfer analysis on MHD blood flow of Casson fluid model due to peristaltic wave

In this article, heat and mass transfer analysis on MHD blood flow of Casson fluid model due to peristaltic wave has been investigated. The governing equations of blood flow for Casson fluid model, temperature, and energy equation have been solved by taking the assumption of long wavelength and neglecting the inertial forces. The resulting coupled differential equations have been solved analytically and the exact solutions are presented. The impact of various pertinent parameters is plotted and discussed. It is found that the influence of magnetic field and fluid parameter shows similar behavior on velocity profile while its behavior is opposite for pressure rise and pressure gradient profile. Trapping phenomena have also taken into account by sketching the streamlines. The expression for pressure rise and friction forces are evaluated numerically.

Analytical Solution of Electro-Osmotic Peristalsis of Fractional Jeffreys Fluid in a Micro-Channel.

The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions of long wavelength, low Reynolds number, and Debye-Hückel linearization, the analytical solutions of pressure gradient, stream function and axial velocity are explored in terms of Mittag-Leffler function by Laplace transform method. The corresponding solutions of fractional Maxwell fluid and generalized second grade fluid are also obtained as special cases. The numerical analysis of the results are depicted graphically, and the effects of electro-osmotic parameter, external electric field, fractional parameters and viscoelastic parameters on the peristaltic flow are discussed.

MHD peristaltic flow of a hyperbolic tangent fluid in a non-uniform channel with heat and mass transfer

The influence of elastic wall properties on the peristaltic transport of a conducting hyperbolic tangent fluid in a non-uniform channel is investigated with heat and mass transfer. The flow is examined in a fixed frame of reference under the assumptions of long wavelength and low Reynolds number. The velocity slip, temperature and concentration jump boundary conditions are considered at the walls. The perturbation method of solution for stream function, velocity, temperature, concentration and the coefficient of heat transfer are obtained in terms of small Weissenberg number. The influence of several pertinent parameters on the flow are discussed by plotting graphs. The trapping phenomenon is also analysed. It is noticed that the size of the trapping bolus increases with increasing the power law index of hyperbolic tangent fluid.

Peristaltic blood flow with gold nanoparticles as a third grade nanofluid in catheter: Application of cancer therapy

Cancer is dangerous and deadly to most of its patients. Recent studies have shown that gold nanoparticles can cure and overcome it, because these particles have a high atomic number which produce the heat and leads to treatment of malignancy tumors. A motivation of this article is to study the effect of heat transfer with the blood flow (non-Newtonian model) containing gold nanoparticles in a gap between two coaxial tubes, the outer tube has a sinusoidal wave traveling down its wall and the inner tube is rigid. The governing equations of third-grade fluid along with total mass, thermal energy and nanoparticles are simplified by using the assumption of long wavelength. Exact solutions have been evaluated for temperature distribution and nanoparticles concentration, while approximate analytical solutions are found for the velocity distribution using the regular perturbation method with a small third grade parameter. Influence of the physical parameters such as third grade parameter, Brownian motion parameter and thermophoresis parameter on the velocity profile, temperature distribution and nanoparticles concentration are considered. The results pointed to that the gold nanoparticles are effective for drug carrying and drug delivery systems because they control the velocity through the Brownian motion parameter Nb and thermophoresis parameter Nt. Gold nanoparticles also increases the temperature distribution, making it able to destroy cancer cells.

Influence of velocity slip and temperature jump conditions on the peristaltic flow of a Jeffrey fluid in contact with a Newtonian fluid

Abstract In this paper, we investigate the peristaltic transport of a two layered fluid model consisting of a Jeffrey fluid in the core region and a Newtonian fluid in the peripheral region. The channel is bounded by permeable heat conducting walls. The analysis is carried out in the wave reference frame under the assumptions of long wave length and low Reynolds number. The analytical expressions for stream function, temperature field, pressure-rise and the frictional force per wavelength in both the regions are obtained. The effects of the physical parameters associated with the flow and heat transfer are presented graphically and analyzed. It is noticed that the pressure rise decrease with increasing slip parameter β in the pumping region (ΔP > 0). The temperature field decreases with increasing Jeffrey number and the velocity slip parameter; whereas the temperature field increases with increasing thermal slip parameter. Furthermore, the size of the trapped bolus increases with increasing Jeffrey number and decreases with increasing slip parameter. We believe that this model can help in understanding the behavior of two immiscible physiological fluids in living objects.

Homotopy Perturbation Method for Creeping Flow of Non-Newtonian Power-Law Nanofluid in a Nonuniform Inclined Channel with Peristalsis

AbstractThis article is an analytic discussion for the motion of power-law nanofluid with heat transfer under the effect of viscous dissipation, radiation, and internal heat generation. The governing equations are discussed under the assumptions of long wavelength and low Reynolds number. The solutions for temperature and nanoparticle profiles are obtained by using homotopy perturbation method. Results for the behaviours of the axial velocity, temperature, and nanoparticles as well as the skin friction coefficient, reduced Nusselt number, and Sherwood number with other physical parameters are obtained graphically and analytically. It is found that as the power-law exponent increases, both the axial velocity and temperature increase, whereas nanoparticles decreases. These results may have applicable importance in the research discussions of nanofluid flow in channels with small diameters under the effect of different temperature distributions.

Nonlinear peristaltic motion of a Jeffery nanofluid with shear stress and MHD effects

A mathematical model based on Jeffrey nanofluid under the effect of magnetic field and thermal radiation parameter for the peristaltic flow is considered in a channel, which is assumed to be in the form of a tapered asymmetric walls. The tapered asymmetry channel is produced by choosing the peristaltic wave train on the non-uniform walls to have different amplitudes and phase but with same wave speed. The analytical expressions for temperature field, nanoparticle fraction field, axial velocity, stream function, pressure gradient and shear stress are derived under the assumptions of long wavelength and low Reynolds number approximations. The salient characteristics of pumping and trapping are discussed with particular focus on the effect of geometry parameters, Hartmann number, thermal radiation parameter and rheological parameter. It has been observed that the pressure rise and axial velocity increase with increasing rheological parameter.DOI: http://dx.doi.org/10.5755/j01.mech.23.3.14481

Outcome of slip features on the peristaltic flow of a Prandtl nanofluid with inclined magnetic field and chemical reaction

This analysis looks at the influence of an inclined magnetic field on the peristaltic motion of a Prandtl nanofluid in an asymmetric channel. The mathematical model is developed through consideration of Joule heating, viscous dissipation and chemical reaction effects. Furthermore, the nanofluid with Brownian motion and thermophoresis effects is studied. The channel walls exhibit the slip conditions for velocity, temperature and nanoparticle volume fraction. Numerical solutions of the problem are developed through the assumptions of long wavelength and low Reynolds number. Graphs are plotted for velocity, temperature, nanoparticle volume fraction and heat transfer rate. The physical interpretation for several parameters of interest is presented in detail. The slip effect reduces the velocity and nanoparticle volume fraction while it enhances the fluid temperature. The opposite effect on fluid velocity and temperature is seen with the inclination of magnetic field.

Influence of Nanoparticles Phenomena on the Peristaltic Flow of Pseudoplastic Fluid in an Inclined Asymmetric Channel with Different Wave Forms

The influence of nanofluid with different wave forms in the presence of inclined asymmetric channel on peristaltic transport of a pseudoplastic fluid is examined. The governing equations for two dimensional and two directional flows of a pseudoplastic fluid along with nanofluid are modeled and then simplified under the assumptions of long wavelength and low Reynolds number approximation. The exact solutions for temperature and nano particle volume fraction are calculated. Series solution of the stream function and pressure gradient are carried out using perturbation technique. The flow quantities have been examined for various physical parameters of interest. It was found that the magnitude value of the velocity profile decreases with an increase in Q and Z and increases in sinusoidal, multisinsoidal, trapezoidal and triangular waves. It was also observed that the size of the trapping bolus decreases with the decrease in the width of the channel d and increases with an increase inx.

Joule heating effects on electromagnetohydrodynamic flow through a peristaltically induced micro-channel with different zeta potential and wall slip

This paper aims to develop a mathematical model for magnetohydrodynamic flow of biofluids through a hydrophobic micro-channel with periodically contracting and expanding walls under the influence of an axially applied electric field. The velocity slip effects have been taken into account at the channel walls by employing different slip lengths due to hydrophobic gating. Different temperature jump factors have also been used to investigate the thermomechanical interactions at the fluid–solid interface. The electromagnetohydrodynamic flow in a microchannel is simplified under the framework of Debye–Hückel linearization approximation. We have derived the closed-form solutions for the linearized dimensionless boundary value problem under the assumptions of long wave length and low Reynolds number. The axial velocity, temperature, pressure distribution, stream function, wall shear stress and the Nusselt number have been appraised for diverse values of the parameters approaching into the problem. Our main focus is to determine the effects of different zeta potential on the axial velocity and temperature distribution under electromagnetic environment. This study puts forward an important observation that the different zeta potential plays an important role in controlling fluid velocity. The study further reveals that the temperature increases significantly with the Joule heating parameter and the Brinkman number (arises due to the dissipation of energy).

Peristaltic flow of an Eyring Prandtl fluid in a diverging tube with heat and mass transfer

The present article reflects the peristaltic motion of an Eyring Prandtl fluid in a diverging tube in the presence of heat and mass transfer. Mathematical Analysis has been carried out by considering the assumptions of long wave length and low Reynolds number. Under these limitations, we obtain resulted non linear system of small values. These have been evaluated analytically using homotopy Perturbation method. The succeeding complex disparity computations are explained for velocity, temperature, concentration field and pressure gradient. The effects of physical parameters on the flow and heat transfer attributes are investigated in detail. Special attention is given to explain the pumping and trapping phenomena in detail. Convergence of solution is clearly shown in the graphical results. It is found that rate of heat transfer and mass transfer decreases with increasing Brashof number. The consequence of many underdeveloped restraint are explicate for five dissimilar impressions. Streamlines in trust at the terminus point of the objective.

Heat transfer and inclined magnetic field analysis on peristaltically induced motion of small particles

In this article, simultaneous effects of heat transfer with a uniform inclined magnetic field on peristaltically induced motion of small particles (particle–fluid) have been analyzed through a uniform channel. Inspired from the applications of two-phase (particle–fluid) flow in biomedical engineering that helps to scrutinize the symmetrical expansion and contraction of smooth muscles (“peristaltic flow”) during the procreation of multiple kinds of biological fluids. Moreover, it is also applicable in different engineering problems such as peristaltic pumping of particle–fluid mixtures and suspension of blood in arteries. The governing flow problem modeled in wave frame with an appropriate use of momentum equation and thermal energy equations, which are simplified for fluid phase and particle by taking the appropriate assumption of long wavelength as well as ignoring the inertial forces. The resulting differential coupled differential equations (ODEs) are linear which are solved analytically and exact solutions are presented for the fluid and particulate phases. The impact of all the physical parameters such as Hartman number, particle volume fraction, amplitude ratio, Froude number, Reynolds number, Prandtl number and Eckert number are discussed vigorously for pressure rise, velocity, streamlines and temperature profile. Furthermore, numerical computation has been used to examine the behavior of peristaltic pumping.

ADOMIAN DECOMPOSITION METHOD FOR MAGNETOHYDRODYNAMIC FLOW OF BLOOD INDUCED BY PERISTALTIC WAVES

The present investigation deals with the application of Adomian decomposition method (ADM) to blood flow through an asymmetric non-uniform channel induced by peristaltic wave in the presence of magnetic field and the velocity slip at the wall. The ADM is applied with an aim to avoid any simplifications and restrictions, which changes non-linearity of the problem as well as to provide analytical solution. The blood flowing through the vessel is assumed to be Newtonian and incompressible with constant viscosity. The analytical expressions for the axial velocity component, streamlines and wall shear stress are presented. The numerical results of these physical quantities are obtained for different values of the Reynolds number, wave number and Hartmann number. The results obtained for different values of the parameters involved in the problem under consideration show that the flow is appreciably influenced by the presence of slip velocity as well as magnetic field. From this study, we conclude that the assumption of long wavelength and low Reynolds number overestimates the flow characteristics even for a small change in the parameters.

Peristaltic Transport of Magnetohydrodynamic Carreau Nanofluid with Heat and Mass Transfer inside Asymmetric Channel

In this work, the peristaltic motion of a nano non-Newtonian fluid which obeys Carreau model through a porous medium inside an asymmetric channel is investigated. The hall current effects with Joule heating and viscous dissipation are considered. The problem is modulated mathematically by a set of nonlinear partial differential equations which describe the conservation of mass, momentum, energy and concentration of nanoparticles. The non-dimensional form of these equations is simplified under the assumption of long wavelength and low Reynolds number, and then resulting equations of coupled nonlinear differential equations are tackled numerically with appropriate boundary conditions. Graphical results are presented for dimensionless velocity, temperature, concentration and pressure gradient in order to illustrate the variations of various parameters of this problem on these obtained solutions.

On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations

We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled Camassa-Holm equations. We give a precise estimate for approximation errors in terms of two small positive parameters measuring the effects of nonlinearity and dispersion. Our results demonstrate that, in the present regime, any solution of the improved Boussinesq equation is split into two waves propagating in opposite directions independently, each of which is governed by the Camassa-Holm equation. We observe that the approximation error for the decoupled problem considered in the present study is greater than the approximation error for the unidirectional problem characterized by a single Camassa-Holm equation. We also consider lower order approximations and we state similar error estimates for both the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.

Thermal radiation impact in mixed convective peristaltic flow of third grade nanofluid

Abstract This paper models the peristaltic transport of magnetohydrodynamic (MHD) third grade nanofluid in a curved channel with wall properties. Combined effects of heat and mass transfer are retained via mixed convection. The present analysis is made in the presence of thermal radiation and chemical reaction. No-slip effect is maintained at the boundary for the velocity, temperature and nanoparticle volume fraction. Resulting formulation is simplified by employing the assumptions of long wavelength and low Reynolds number approximations. Results of axial velocity, temperature, nanoparticle mass transfer and heat transfer are studied graphically. Results reveal increment in fluid velocity for larger values of heat transfer Grashof number. There is reduction in nanoparticle mass transfer with the increase in thermophoresis parameter.

Growth of Vapour Bubble Flow inside a Symmetric Vertical Cylindrical Tube

The paper introduces the incompressible Newtonian fluid with heat transfer in a vertical cylindrical tube under the assumptions of long wavelength and low Reynolds number. The system of mass, momentum, and energy equations are solved analytically. The velocity and temperature field are obtained for two-phase densities. The growth of vapour bubble and its velocity between two-phase densities are obtained for first time under the effect of Grashof number and constant heating source. The obtained results are compared with experiment and Mohammadein at all model with good agreement.

Impact of curvature on the mixed convective peristaltic flow of shear thinning fluid with nanoparticles

The aim of the present analysis is to discuss the mixed convective peristaltic flow of shear thinning hyperbolic tangent fluid under the effects of nanoparticles in a curved channel. The model considered for the nanofluid is to analyze the effects of Brownian motion and thermophoresis parameter. The problem is formulated under the assumptions of long wavelength and low Reynolds number and then solved analytically using the homotopy perturbation method (HPM). The substantial features of related parameters are examined by sketching graphs. The most important observation of the analysis is that the velocity profiles are not symmetric about the central line of the curved channel.

Stimulation of metallic nanoparticles under the impact of radial magnetic field through eccentric cylinders: A useful application in biomedicine

This paper represents a new model of magnetohydrodynamic (MHD) peristaltic flow of nanofluid by considering the blood as the base fluid and copper and silver as the nanoparticles through eccentric annuli. An appropriate model of peristaltic pumping is introduced and it is encouraged due to the fact that thread infusion within the human body is a promising strategy for setting medical implants with least surgical trauma. The central cylinder is rigid and moving with consistent velocity V while the outlying tube has a sinusoidal wave going down through its wall. A magnetic field is imposed in radial direction to enhance the amplitude of wave (for synchronization avail in ECG). The complicated flow model equations are first simplified under the assumptions of long wavelength and low Reynolds number. Then series solutions are obtained for resulting system. The innovation with distinct sundry parameters are discussed via graphical illustrations. Comparison among the pure blood, silver blood and copper blood is presented and analyzed. It is also revealed that inclusion of nanoparticles enlarge the velocity of fluid.