Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer

In the present paper we discuss the magnetohydrodynamic （MHD） peristaltic flow of a hyperbolic tangent fluid model in a vertical asymmetric channel under a zero Reynolds number and long wavelength approximation. Exact solution of the temperature equation in the absence of dissipation term has been computed and the analytical ex- pression for stream function and axial pressure gradient are established. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The expression for pressure rise has been computed numerically. The physical features of pertinent parameters are analyzed by plotting graphs and discussed in detail.

Peristaltic motion of third grade fluid in curved channel

＂ Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a single ordinary differential equation in a stream function by using the assumptions of long wavelength and low Reynolds number. This differential equation is solved numerically by employing the built-in routine for solving nonlinear boundary value problems （BVPs） through the software Mathematica. In addition, the analytic solutions for small Deborah number are computed with a regular perturbation technique. It is noticed that the symmetry of bolus is destroyed in a curved channel. An intensification in the slip effect results in a larger magnitude of axial velocity. Further, the size and circulation of the trapped boluses increase with an increase in the slip parameter. Different from the case of planar channel, the axial velocity profiles are tilted towards the lower part of the channel. A comparative study between analytic and numerical solutions shows excellent agreement.

Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel

In this paper, the influence of heat transfer and induced magnetic field on peristaltic flow of a Johnson-Segalman fluid is studied. The purpose of the present investigation is to study the effects of induced magnetic field on the peristaltic flow of non-Newtonian fluid. The two-dimensional equations of a Johnson-Segalman fluid are simplified by assuming a long wavelength and a low Reynolds number. The obtained equations are solved for the stream function, magnetic force function, and axial pressure gradient by using a regular perturbation method. The expressions for the pressure rise, temperature, induced magnetic field, pressure gradient, and stream function are sketched and interpreted for various embedded parameters.

On the gating of mechanosensitive channels by fluid shear stress

Mechanosensation is an important process in biological fluid-structure interaction. To understand the biophysics underlying mechanosensation, it is essential to quantify the correlation between membrane deformation, membrane tension, external fluid shear stress, and conformation of mechanosensitive (MS) channels. Smoothed dissipative particle dynamics (SDPD) simulations of vesicle/cell in three types of flow configurations are conducted to calculate the tension in lipid membrane due to fluid shear stress from the surrounding viscous flow. In combination with a simple continuum model for an MS channel, SDPD simulation results suggest that shearing adhered vesicles/cells is more effective to induce membrane tension sufficient to stretch MS channels open than a free shear flow or a constrictive channel flow. In addition, we incorporate the bilayer-cytoskeletal interaction in a two-component model to probe the effects of a cytoskeletal network on the gating of MS channels.

Three-dimensional channel flow of second grade fluid in rotating frame

An analysis is performed for the hydromagnetic second grade fluid flow between two horizontal plates in a rotating system in the presence of a magnetic field. The lower sheet is considered to be a stretching sheet, and the upper sheet is a porous solid plate. By suitable transformations, the equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations. A series of solutions to this coupled non-linear system are obtained by a powerful analytic technique, i.e., the homotopy analysis method （HAM）. The results are presented with graphs. The effects of non-dimensional parameters R, A, M2, a, and K2 on the velocity field are discussed in detail.

Unsteady Flow of a Dusty Visco-Elastic Fluid Through an Incliend Channel

The present discussion deals with the study of an unsteady flow of a dusty fluid through an inclined channel under the influence of pulsatile pressure gradient along with the effect of a uniform magnetic field. The analytical solutions of the problem are obtained using variable separable and Fourier transform techniques. The graphs drawn for the velocity fields of both fluid and dust phase under the effect of Reynolds number. The velocity profiles for the liquid and the dust particles decreases at different values of time t increases. As the visco-elastic parameter λ increases the velocity of the liquid and the dust particles deceases. When relaxation time parameter σ increases, the velocity of the liquid and dust particles decreases.

BASIC EQUATIONS OF TURBULENT FLOW FOR VARIABLE DENSITY AND VARIABLE VISCOSITY NEWTONIAN FLUID IN OPEN CHANNEL

In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method （HAM） is used＇to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu＇s model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations axe transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α（t） from the initial state α0 to the final state al. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.

Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary conditions

This work is concerned with the peristaltic transport of the Johnson-Segalman fluid in an asymmetric channel with convective boundary conditions. The mathematical modeling is based upon the conservation laws of mass, linear momentum, and energy. The resulting equations are solved after long wavelength and low Reynolds number are used. The results for the axial pressure gradient, velocity, and temperature profiles are obtained for small Weissenberg number. The expressions of the pressure gra-dient, velocity, and temperature are analyzed for various embedded parameters. Pumping and trapping phenomena are also explored.

Analytic solution to the micropolar-fluid flow through a semi-porous channel with an expanding or contracting wall

The flow of a micropolar fluid in a semi-porous channel with an expanding or contracting wall is investigated. The governing equations are reduced to ordinary ones by using similar transformations. To get the analytic solution to the problem, the homotopy analysis method （HAM） is employed to obtain the expressions for velocity fields. Graphs are sketched and discussed for various parameters, especially the effect of the expansion ratio on velocity and micro-rotation fields.

Run-Up Flow of a Maxwell Fluid through a Parallel Plate Channel

We consider the flow of an incompressible viscous Maxwell fluid between two parallel plates, initially induced by a constant pressure gradient. The pressure gradient is withdrawn and the upper plate moves with a uniform velocity while the lower plate continues to be at rest. The arising flow is referred to as run-up flow. The unsteady governing equations are solved as initial value problem using Laplace transform technique. The expression for velocity, shear stresses on both plates and discharge are obtained. The behavior of the velocity, shear stresses and mass flux has been discussed in detail with respect to variations in different governing flow parameters and is presented through graphs.

Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect

The present study deals with the analysis of heat transfer of the unsteady Maxwell nanofluid flow in a squeezed rotating channel of a porous extensile surface subject to the velocity and thermal slip effects incorporating the theory of heat flow intensity of Cattaneo-Christov model for the expression of the energy distribution in preference to the classical Fourier’s law. A set of transformations is occupied to renovate the current model in a system of nonlinear ordinary differential equations that are numerically decoded with the help of MATLAB integrated function bvp4c. The effects of various flow control parameters are investigated for the momentum, temperature and diffusion profiles, as well as for the wall shearing stress and the heat and mass transfer. The results are finally described from the material point of view. A comparison of heat flux models of Cattaneo-Christov and Fourier is also performed. An important result from the present work is that the squeezing parameter is strong enough in the middle of the channel to retard the fluid flow.

Heat and Mass Transfer on Non-Newtonian Peristaltic Flow in a Channel in Presence of Magnetic Field: Analytical and Numerical Analysis

A study has been arranged to investigate the flow of non-Newtonian fluid in a vertical asymmetrical channel using peristalsis. The porous medium allows the electrically conductive fluid to flow in the channel, while a uniform magnetic field is applied perpendicular to the flow direction. The analysis takes into account the combined influence of heat and mass transfer, including the effects of Soret and Dufour. The flow’s non-Newtonian behavior is characterized using a Casson rheological model. The fluid flow equations are examined within a wave frame of reference that has a wave velocity. The analytic solution is examined using long wavelengths and a small Reynolds number assumption. The stream function, temperature, concentration and heat transfer coefficient expressions are derived. The bvp4c function from MATLAB has been used to numerically solve the transformed equations. The flow characteristics have been analyzed using graphs to demonstrate the impacts of different parameters.

Fluid Flow and Heat Transfer Charateristics in a 180-deg Round Turned Channel with a Perforated Divider

This study provided a new configuration of the 180-deg round turned channel with a perforated divider, as well as numerically investigated the effect of perforations, including the diameter of perforation and the angel of perforation, on the fluid flow and heat transfer. The numerical results appeared in good agreement with previous experimental data under the same operating conditions. The results indicated that large size and positive angle of perforation changed the fluid flow pattern and the local Nusselt-number distribution fundamentally. It is noteworthy that a more uniform distribution of Nusselt-number was achieved by increasing the diameter of perforation.

Viscoelastic Effects on Unsteady Two-Dimensional and Mass Transfer of a Viscoelastic Fluid in a Porous Channel with Radiative Heat Transfer

An analysis of oscillatory flow of a viscoelastic fluid and mass transfer along a porous oscillating channel with radiative heat transfer in presence of first-order chemical reaction is considered. The problem is concerned with the flow through a channel in which the viscoelastic fluid is injected on one boundary of the channel with a constant velocity, while it is sucked off at the other boundary with the same velocity. The two boundaries are considered to be in close contact with the two plates placed parallel to each other. The effect of temperature oscillations at the plate (upper wall) where the suction takes place is taken into consideration. The plates are supposed to be oscillating with a given velocity in their own planes. Analytical expressions for velocity profile, the temperature, concentration profile, wall shear stress on the upper wall are obtained. The profiles of the velocity and skin friction have been presented graphically for different values of the viscoelastic parameters with the combination of the other flow parameters encountered in the problem under investigation. It is observed that velocity decrease with the increasing values of the viscoelastic parameter in comparison with Newtonian fluid. Also, the wall shear stress increase with the increasing values of the viscoelastic parameter.

Rotating electroosmotic flow of an Eyring fluid

A perturbation analysis is presented in this paper for the electroosmotic (EO) flow of an Eyring fluid through a wide rectangular microchannel that rotates about an axis perpendicular to its own. Mildly shear-thinning rheology is assumed such that at the leading order the problem reduces to that of Newtonian EO flow in a rotating channel, while the shear thinning effect shows up in a higher-order problem. Using the relaxation time as the small ordering parameter, analytical solutions are deduced for the leading- as well as first-order problems in terms of the dimensionless Debye and rotation parameters. The velocity profiles of the Ekman-electric double layer (EDL) layer, which is the boundary layer that arises when the Ekman layer and the EDL are comparably thin, are also deduced for an Eyring fluid. It is shown that the present perturbation model can yield results that are close to the exact solutions even when the ordering parameter is as large as order unity. By this order of the relaxation time parameter, the enhancing effect on the rotating EO flow due to shear-thinning Eyring rheology can be significant.

Unsteady flow and heat transfer of porous media sandwiched between viscous fluids

The problem of unsteady oscillatory flow and heat transfer of porous medin sandwiched between viscous fluids has been considered through a horizontal channel with isothermal wall temperatures. The flow in the porous medium is modeled using the Brinkman equation. The governing partial differential equations are transformed to ordinary differential equations by collecting the non-periodic and periodic terms. Closed-form solutions for each region are found after applying the boundary and interface conditions. The influence of physical parameters, such as the porous parameter, the frequency parameter, the periodic frequency parameter, the viscosity ratios, the conductivity ratios, and the Prandtl number, on the velocity and temperature fields is computed numerically and presented graphically. In addition, the numerical values of the Nusselt number at the top and bottom walls are derived and tabulated.

Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching of the plate

In this communication a generalized three- dimensional steady flow of a viscous fluid between two infinite parallel plates is considered. The flow is generated due to uniform stretching of the lower plate in x- and y-directions. It is assumed that the upper plate is uniformly porous and is subjected to constant injection. The governing system is fully coupled and nonlinear in nature. A complete analytic solution which is uniformly valid for all values of the dimensionless parameters β Re and λ is obtained by using a purely analytic technique, namely the homotopy analysis method. Also the effects of the parameters β Re and λ on the velocity field are discussed through graphs.

Scaling of the bubble/slug length of Taylor flow in a meandering microchannel

In order to reduce or avoid the fluctuations from interface breakup, a meandering microchannel with curved multi-bends(44 turns) is fabricated, and investigations of scaling bubble/slug length in Taylor flow in a rectangular meandering microchannel are systematically conducted. Based on considerable experimental data,quantitative analyses for the influences of two important characteristic times, liquid phase physical properties and aspect ratio are made on the prediction criteria for the bubble/slug length of Taylor flow in a meandering microchannel. A simple principle is suggested to predict the bubble formation period by using the information of Rayleigh time and capillary time for six gas–liquid systems with average deviation of 10.96%. Considering physical properties of the liquid phase and cross-section configuration of the rectangular mcirochannel,revised scaling laws for bubble length are established by introducing Ca, We, Re and W/h whether for the squeezing-driven or shearing-driven of bubble break. In addition, a simple principle in terms of Garstecki-type model and bubble formation period is set-up to predict slug lengths. A total of 107 sets of experimental data are correlated with the meandering microchannel and operating range: 0.001 b CaTPb 0.05, 0.06 b WeTPb 9.0,18 b ReTPb 460 using the bubble/slug length prediction equation from current work. The average deviation between the correlated data and the experimental data for bubble length and slug length is about 9.42% and9.95%, respectively.

Existence of a Hartmann layer in the peristalsis of Sisko fluid

Analytical solutions for the peristaltic flow of a magneto hydrodynamic （MHD） Sisko fluid in a channel, under the effects of strong and weak magnetic fields, are presented. The governing nonlinear problem, for the strong magnetic field, is solved using the matched asymptotic expansion. The solution for the weak magnetic field is obtained using a regular perturbation method. The main observation is the existence of a Hartman boundary layer for the strong magnetic field at the location of the two plates of the channel. The thickness of the Hartmann boundary layer is determined analytically. The effects of a strong magnetic field and the shear thinning parameter of the Sisko fluid on the velocity profile are presented graphically.