Slip effects on the peristaltic transport of MHD fluid with variable viscosity

This Letter concerns with the peristaltic analysis of MHD viscous fluid in a two-dimensional channel with variable viscosity under the effect of slip condition. A long wavelength and low Reynolds number assumption is used in the problem formulation. An exact solution is presented for the case of hydrodynamic fluid while for magnetohydrodynamic fluid a series solution is obtained in the small power of viscosity parameter. The salient features of pumping and trapping phenomena are discussed in detail through the numerical integration. It is noted that an increase in the slip parameter decreases the peristaltic pumping region. Moreover, the size of trapped bolus decreases by increasing the slip parameter.     

MHD flow study of viscous fluid through a complex wavy curved surface due to biomimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity(Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic(Hartmann number) and porosity(Darcy number)parameters on the rheological features of peristaltic transportation are argued in detailed(in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid,assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first-and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress,tangential component of the extra-stress tensor, pumping and trapping phenomena.     

Analytical Solution for Peristaltic Transport of Viscous Nanofluid in an Asymmetric Channel with Full Slip and Convective Conditions

The peristaltic flow of nanofluids is a relatively new area of research. Scientists are of the opinion that the no-slip conditions at the boundaries are no longer valid and consequently, the first and the second order slip conditions should be addressed. In this paper, the effects of slip conditions and the convective boundary conditions at the boundary walls on the peristaltic flow of a viscous nanofluid are investigated for. Also, the exact analytical solutions are obtained for the model. The obtained results are presented through graphs and discussed. The results reveal that the two slip parameters have strong effects on the temperature and the nanoparticles volume fraction profiles. Moreover, it has been seen that the temperature and nanoparticles volume fraction profiles attain certain values when the first slip condition exceeds a specified value. However, no limit value for the second slip parameter has been detected. Further, the effects of the various emerging parameters on the flow and heat transfer characteristics have been presented.     

Peristaltic transport in a slip flow

Continuum-mechanic derivation of the entrainment of rarefied gases induced by a surface wave along walls (or peristaltic transport) in a confined parallel-plane microchannel is conducted by the perturbation method. Both no-slip and slip flow cases are investigated with the former ones matched with the previous approach by Fung and Yih. Critical reflux values due to first order slip-flow effects become trivial for the free pumping case, and decrease due to second order slip-flow effects after we compared them with no-slip cases. Received 27 August 1999 and Received in final form 10 January 2000     

Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet

The entrained flow of an electrically conducting non-Newtonian, viscoelastic second grade fluid due to an axisymmetric stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equation into an ordinary differential equation. The issue of paucity of boundary conditions is addressed, and an effective numerical scheme has been adopted to solve the obtained differential equation even without augmenting the boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and skin friction coefficient. It is observed that in presence of slip, the velocity decreases with an increase in the magnetic parameter. That is, the Lorentz force which opposes the flow leads to enhanced deceleration of the flow. Moreover, it is interesting to find that as slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid.     

Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effects of both magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel are studied analytically and numerically. The channel asymmetry is generated by propagation of waves on the channel walls travelling with different amplitudes, phases but with the same speed. The long wavelength and low Reynolds number assumptions are considered in obtaining solution for the flow. The flow is investigated in a wave frame of reference moving with velocity of the wave. Closed form expressions have been obtained for the stream function and the axial velocity component in fixed frame. The effects of phase difference, Knudsen number and magnetic field on the pumping characteristics and velocity field are discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.     

Slip flow of MHD Casson fluid in an inclined channel with variable transport properties

Due to the instructive role of the peristaltic phenomenon in the human body, interests have been developed in recent years towards peristaltic transport with various thermo-physical features. The current investigation reveals the effects of the magnetic field and variable transport properties on the peristaltic transport of a Casson fluid slip flow through an inclined channel. Nonlinear coupled partial differential equations regulate the fluid flow. Through the perturbation method, the momentum and energy equations are solved for small values of variable viscosity and thermal conductivity, and the closed-form solution is obtained for mass transfer. The impact on physiological quantities of related parameters of interest is evaluated and discussed via graphs. The results obtained for the current flow represent some interesting behaviors which have applications in the biomedical field.     

Numerical simulation of Electrokinetically Driven Peristaltic Pumping of Silver-Water Nanofluids in an asymmetric microchannel

This article intends to focus on the theoretical and numerical investigation of the peristaltic pumping of water-based silver nanofluid in the presence of electroosmotic forces. The investigation is carried out in an asymmetric microchannel subject to the influence of mixed convection and viscous dissipation. No-slip boundary conditions for velocity, temperature, and nanoparticle volume fraction are imposed on channel walls. The lubrication approach is utilized to simplify the normalized constitutive equations. The distribution of electric potential in the electric double layer is characterized by Poisson-Boltzmann ionic distribution which is further linearized by Debye-Hückel approximation. Nanofluid properties are predicted by a combination of the Buongiorno two-phase mixture model and homogeneous flow model. Additionally, the effective thermal conductivity and dynamic viscosity of silver-water nanofluid are characterized by the Corcione model. Silver nanoparticles of 20nm diameter are utilized in this suspension. The transformed set of nonlinear and coupled equations is numerically executed for axial velocity, temperature, and nanoparticle volume fraction by employing the mathematical software Maple 17. Pumping and trapping phenomena are also investigated. A comparison between the thermal conductivity of nanofluid predicted by the Corcione model and the Maxwell model is further presented. The influence of various flow parameters is outlined through graphical results. It has been observed that the thermal conductivity of silver-water nanofluid enhances with increasing nanoparticle volume fraction and temperature but decreases for larger sized nanoparticles. Moreover, the heat transfer rate rises significantly when smaller silver nanoparticles are suspended in water. Furthermore, the temperature of nanofluid is directly related to the Debye length parameter and the Helmholtz- Smoluchowski velocity parameter.     

Peristaltic Motion of a Particle-Fluid Suspension in a Planar Channel

We analyze the mechanics of peristaltic pumpingof a particle-fluid suspension in a channel. Aperturbation series (to second order) in dimensionlesswave number of an infinite harmonic travelling wave is used to obtain an explicit form for thevelocities and a relation between the flow rate and thepressure gradient in terms of the Reynolds number,concentration of the particles, suspension parameters, and the occlusion. We discuss the effect of theconcentration of the particles, the Reynolds number, andthe wave number on the pressure rise, peristalticpumping, augmented pumping, and backward pumping. We also discuss the phenomenon oftrapping.     

On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium

The effect of elasticity of the flexible walls on the MHD peristaltic flow of a Newtonian fluid in a two-dimensional porous channel with heat transfer has been studied under the assumptions of long-wavelength and low-Reynolds number. The analytical solution has been obtained for the stream function, temperature and heat transfer coefficient. The effect of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The numerical results show that the trapped bolus increases in size and more trapped bolus appears with increasing permeability parameter, elastic tension and mass characterizing parameters but decreases for large values of Hartmann number.     

Entropy generation analysis for peristaltically driven flow of hybrid nanofluid

Present study investigates entropy generation analysis for peristaltic motion of hybrid nanofluid. Hybrid nanofluid is composed of iron-oxide and copper nanoparticles suspended in water. Effects of Hall current, Ohmic heating and mixed convection are taken into account. Governing equations are simplified by utilizing lubrication approach. The numerical solutions for resulting system of differential equations are obtained with the aid of Shooting method. Attention has been given to the analysis of hybrid nanoparticles, Hall parameter and Grashoff number on entropy generation, heat transfer rate, velocity profile and pressure gradient. Outcomes reveal that insertion of nanoparticles decreases the temperature of hybrid nanofluid. It is found that increase in Hall parameter reduces the heat transfer rate at wall. Increment in Hall parameter reduces the entropy generation. Velocity and pressure gradient increases by enhancing Grashoff number. It is believed that the present flow model can prove useful in improving the efficiency of similar thermodynamical systems.     

Oblique stagnation slip flow of a micropolar fluid towards a stretching/shrinking surface: A stability analysis

A numerical solution is obtained for the steady oblique stagnation-point flow of a micropolar fluid over a stretching or shrinking surface with velocity slip condition. Results are obtained for representative values of slip parameter, micropolar parameter and stretching/shrinking parameter for strong particle interaction micropolar fluid. Dual solutions are found for the case of shrinking surface. An analysis of stability of these dual solutions shows that the solution branch that proceeds to large stretching case is stable. The streamlines are not symmetric for the oblique stagnation-point flow and reversed flow are observed near to the shrinking surface. The streamlines plots show that increase of slip parameter will reduce/eliminate the existing of rotating flow near the surface that caused by the shrinking effect.     

Electro-osmotic nanofluid flow in a curved microchannel

Biological mechanisms offer significant improvement in the efficiency of next generation energy systems. Motivated by new developments in distensible pumping systems, ionic electro-kinetic manipulation and nanoscale liquids (”nanofluids”), in the present study a mathematical model is developed to simulate the entropy generation and electro-osmotic transport of nanofluids in a curved deformable microchannel driven by peristaltic transport. Both thermal and species (nano-particle) buoyancy effects are included and Soret and Dufour cross-diffusion effects. The appropriate conservation equations are normalized with scaled variables and the resulting dimensionless nonlinear boundary value problem is solved in a transformed coordinate system. Simplification of the mathematics is achieved via lubrication approximations and low zeta potential (Debye Hückel linearization). The effects of various parameters, i.e. electro-osmotic velocity, EDL (electrical double layer) thickness and zeta potential ratio on velocity profile and temperature profiles are computed. The effects of Brinkman number (viscous heating parameter) and Joule (electrical field heating) parameter on nano-particle concentration profiles are also simulated. The micro-channel curvature effects on the nanofluid flow characteristics and thermal characteristics are also computed. Furthermore, streamline patterns, temperature contours, nano-particles concentration contours and entropy generation rate contours are plotted for various curvature parameters. Results indicate that the curvature of the channel and electro-osmotic body force influence strongly the sources of entropy generation rate. The study finds applications in bio-inspired electro-osmotic nanofluid pumping in microscale energy applications.     

Influence of radiative heat flux in nonlinear convection of quartic order in Casson fluid past a vertical permeable plate with variable suction and Hall current

The current study centralizes on unsteady free convection slip flow of Casson fluid past a vertical permeable plate with Hall current, radiative heat flux, and variable suction. The nonlinear convection is subjected to quartic order. Perturbation method is used to convert the non-linear coupled partial differential equation of the momentum and energy to a system of ordinary differential equations. The dimensionless governing equations are solved analytically for velocity and temperature profiles. The graphs are plotted for sundry parameters for variations in the distinct flow fields w.r.t distance from the plate. Variation in the skin friction for the axial and transverse cases are presented in the form of graphs for various parameters. It is observed that with the increase in the order of non-linear convection and value of radiation parameter, the velocity field increases in Casson fluid. The increase in heat absorption parameter and Prandtl number decreases the temperature profile and increase in radiative heat flux parameter increases the temperature profile.     

Effect of Hall and ion-slip on the peristaltic transport of nanofluid: A biomedical application

The peristaltic flow of viscous nanofluid in a channel with compliant walls is examined. The flow analysis is presented in the presence of Hall and ion-slip effects. The resulting equations through long wavelength and low Reynolds number approaches are solved. Stream function is obtained in closed form. Attention has been given to the influence of Brownian motion, thermophoresis and Hall and ion slip parameters on the velocity, temperature and concentration profiles. The results show an affective increase in the temperature and nanoparticles concentration with the increase in the strength of Brownian motion effects. Similar results are observed for Hall and ion slip parameters. Further heat transfer coefficient is an increasing function of Hall and ion-slip parameters. Also decrease in the size of trapped bolus is shown for Hall and ion-slip parameters.     

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

We discuss the effects of the surface slip on streamline patterns and their bifurcations for the peristaltic transport of a Newtonian fluid. The flow is in a two-dimensional symmetric channel or an axisymmetric tube. An exact expression for the stream function is obtained in the wave frame under the assumptions of long wavelength and low Reynolds number for both cases. For the discussion of the particle path in the wave frame, a system of nonlinear autonomous differential equations is established and the methods of dynamical systems are used to discuss the local bifurcations and their topological changes. Moreover, all types of bifurcations and their topological changes are discussed graphically. Finally, the global bifurcation diagram is used to summarize the bifurcations.     

Effects of Thermal Radiation and Slip Mechanism on Mixed Convection Flow of Williamson Nanofluid Over an Inclined Stretching Cylinder

The current investigation highlights the mixed convection slip flow and radiative heat transport of uniformly electrically conducting Williamson nanofluid yield by an inclined circular cylinder in the presence of Brownian motion and thermophoresis parameter.A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected.The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations.The reduced nonlinear ordinary differential equations are then solved numerically by Runge-Kutta-Fehlberg fifth-order method with shooting technique.The effects of magnetic field,Prandtl number,mixed convection parameter,buoyancy ratio parameter,Brownian motion parameter,thermophoresis parameter,heat generation/absorption parameter,mass transfer parameter,radiation parameter and Schmidt number on the skin friction coefficient and local Nusselt are analyzed and discussed.It is found that the velocity of the fluid decreases with decrease in curvature parameter,whereas it increases with mixed convection parameter.Further,the local Nusselt number decreases with an increase in the radiation parameter.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

Peristaltic Flow of Shear Thinning Fluid via Temperature-Dependent Viscosity and Thermal Conductivity

In this paper Williamson fluid is taken into account to study its peristaltic flow with heat effects. The study is carried out in a wave frame of reference for symmetric channel. Analysis of heat transfer is accomplished by accounting the effects of non-constant thermal conductivity and viscosity and viscous dissipation. Modeling of fundamental equations is followed by the construction of closed form solutions for pressure gradient, stream function and temperature while assuming Reynold's number to be very low and wavelength to be very long. Double perturbation technique is employed, considering Weissenberg number and variable fluid property parameter to be very small. The effects of emerging parameters on pumping, trapping, axial pressure gradient, heat transfer coefficient, pressure rise, velocity profile and temperature are analyzed through the graphical representation. A direct relation is observed between temperature and thermal conductivity whereas the indirect proportionality with viscosity. The heat transfer coefficient is lower for a fluid with variable thermal conductivity and variable viscosity as compared to the fluid with constant thermal conductivity and constant viscosity.