The Streaming Potential of Fluid through a Microchannel with Modulated Charged Surfaces

In this paper, the effects of asymmetrically modulated charged surfaces on streaming potential, velocity field and flow rate are investigated under the axial pressure gradient and vertical magnetic field. In a parallel-plate microchannel, modulated charged potentials on the walls are depicted by the cosine function. The flow of incompressible Newtonian fluid is two-dimensional due to the modulated charged surfaces. Considering the Debye–Hückel approximation, the Poisson–Boltzmann (PB) equation and the modified Navier–Stokes (N-S) equation are established. The analytical solutions of the potential and velocities (u and v) are obtained by means of the superposition principle and stream function. The unknown streaming potential is determined by the condition that the net ionic current is zero. Finally, the influences of pertinent dimensionless parameters (modulated potential parameters, Hartmann number and slip length) on the flow field, streaming potential, velocity field and flow rate are discussed graphically. During the flow process and under the impact of the charge-modulated potentials, the velocity profiles present an oscillating characteristic, and vortexes are generated. The results show that the charge-modulated potentials are beneficial for the enhancement of the streaming potential, velocity and flow rate, which also facilitate the mixing of fluids. Meanwhile, the flow rate can be controlled through the use of a low-amplitude magnetic field.

Energy transport in axisymmetric flow on a rotating cylinder with heat source/sink and chemical reaction

In this article, a thermal analysis is conducted for the axisymmetric flow of viscous nanofluid induced by torsional motion of cylinder. Here the rotation of the cylinder is axially dependent. The impression of heat source/sink with chemical reaction is perceived on the thermal and concentration boundary layer, while the consequence of magnetic field is observed on the fluid flow. In addition, we utilized a two-phased model for nanofluids, namely Buongiorno's model to compute the outcomes of the Soret effect and Brownian diffusion. The non-dimensional ordinary differential equations (ODEs) are obtained by employing the similarity transformation into governing partial differential equations (PDEs). We employed a built-in function, viz. bvp5c, a finite difference method in Matlab®, to solve the BVPs. The acquired results showed that the axial component of the velocity field occurred as a wall jet phenomenon, which is due to an axial pressure gradient. The axial flow and energy of the system are lessened; however, the peak of the wall jet is amplified for higher values of Reynolds number, but the converse trend is observed in the case of the magnetic parameter. The influence of pertinent parameters is also scrutinized for the wall-shear stress, local Nusselt, and Sherwood number for a selected range of Reynolds number, i.e., [Formula: see text] Furthermore, the consequences of the magnetic field have been succinctly observed on the flow, temperature, and concentration profiles. It is concluded that the magnetic field creates a resisting force that causes a reduction in the velocity fields, while temperature profile is enhanced because of the thermal conductivity of nanofluid. The impression of heat source/sink elevated the energy of system, whereas chemical reaction reduced the concentration field.

Peristaltic-Ciliary Flow of A Casson Fluid through An Inclined Tube

The paper is concerned with the peristaltic-ciliary transport of a viscoplastic fluid (Casson fluid) through an inclined cylindrical tube. The peristalsis-cilia induced motion is analysed in the moving frame of reference under the lubrication approximations. Solutions to the flow characteristics petering to yielded and unyielded regions are obtained. The effects of various physical parameters on the axial velocity, the pumping characteristics, the pressure rise, and the frictional force over one wavelength, along with the trapping phenomenon are presented through graphs. Further, the peristaltic flow and peristaltic-ciliary flow results are compared. It is noticed that the axial velocity and the size of trapping bolus in the unplug flow region decrease with an increase in the yield stress. In addition, the axial velocity and the axial pressure gradient in the peristaltic-ciliary pumping are higher than those in the peristaltic pumping.

Heat Transfer Study of the Ferrofluid Flow in a Vertical Annular Cylindrical Duct under the Influence of a Transverse Magnetic Field

We studied the laminar fully developed ferrofluid flow and heat transfer phenomena of an otherwise magnetic fluid into a vertical annular duct of circular cross-section and uniform temperatures on walls which were subjected to a transverse external magnetic field. A computational algorithm was used, which coupled the continuity, momentum, energy, magnetization and Maxwell’s equations, accompanied by the appropriate conditions, using the continuity–vorticity–pressure (C.V.P.) method and a non-uniform grid. The results were obtained for different values of field strength and particles’ volumetric concentration, wherein the effects of the magnetic field on the ferrofluid flow and the temperature are revealed. It is shown that the axial velocity distribution is highly affected by the field strength and the volumetric concentration, the axial pressure gradient depends almost linearly on the field strength, while the heat transfer significantly increases due to the generated secondary flow.

Investigations of hydraulic transient flows in pressurized pipeline based on 1D traditional and 3D weakly compressible models

Transient flow characteristics and dissipation mechanism in pressurized pipeline were investigated based on 1D friction models and 3D turbulence models, where the pressure–density model was combined into the 3D continuity equation allowing for the elasticity of the fluid and the pipes. The applicability of 3D realizable k–ε and 3D SST (shear stress transport) k–ω turbulence models was verified with comparison to 1D traditional water hammer models and the experimental data for fast closing of the valve in the reservoir–pipe–valve system. The valve closure rule was instantaneously carried out using the grid slip CFD (computational fluid dynamics) technique. The SST k–ω turbulence model has the highest accuracy in predicting the pressure attenuation of transient flows. The 3D detailed flow field confirms that the asymmetric flows induced by the change of valve opening within approximately three-fourths of the pipe inner diameter before the valve are captured. In the pressure wave cycles, the unsteady inertia, axial pressure gradient, viscous shear stress and turbulent shear stress mainly influence the velocity variations. During the pressure wave propagation, the viscous and turbulent dissipation are critical in the pressure attenuation in the wall region; the viscous dissipation is mainly concentrated in the viscous sublayer, while the turbulent dissipation increases to the maximum values at y+ = 13–23.

Impact of Homogeneous/Heterogeneous Reactions and Convective Conditions on Peristaltic Fluid Flow in a Symmetric Channel

Simultaneous impacts of homogeneous and heterogeneous reaction and Joule heating in magnetohydrodynamic (MHD) peristaltic flow of viscous fluid in a symmetric channel are analyzed in this investigation. Attention has been focused on designing and simulating a mathematical model for a viscous fluid in presence of viscous dissipation. Long wavelength approximation in wave frame analysis is implemented. Expressions for the stream function, axial pressure gradient, temperature, heat transfer coefficient and concentration are derived and discussed. In addition, the trapping phenomenon is analyzed. The effects of the physical quantities of concern are viewed with a special focus on homogeneous and heterogeneous reaction and convective conditions for the transfer of heat at the walls. It is observed that the pressure rise first increases and then decreases with an increase in amplitude ratio. Effects of Brinkman and Hartmann numbers on temperature are quite analogous and a temperature rise is observed, however, temperature decays for the increased value of Biot number. Moreover, fluid concentration decreases when the value of the homogeneous reaction parameter is increased.

Investigation of electroosmosis flow of copper nanoparticles with heat transfer due to metachronal rhythm

A mathematical model is explored to establish the electroosmotic flow for Cu-wa-ter nanoliquids within a ciliated symmetric micro-channel, the flow is established with aid of ciliary motion and axial pressure gradient. Nanofluid comprise of Cu as a nanofluid particles and water as base fluid. Maxwell-Garnelt model is exploited for viscosity and thermal conductivity of nanoliquid. Magnetic field is applied in the transverse direction and external electric field is enforced in the axial direction. Equations of motion are simplified for nanofluid flow in the micro-channel by employing low Reynolds number and long wavelength approximation theory. Crucial exact analytical expression are gathered for electric potential, temperature profile, axial velocity, volume flux, pressure gradient, stream function, and result for pressure rise per wavelength explored numerically. The influence of crucial flow parameters on, flow behaviour, pumping phenomena, and temperature profile are thoroughly investigated.

Study of electro-osmotic nanofluid transport for scraped surface heat exchanger with heat transfer phenomenon

In this study a novel mathematical model for electroosmotic flow for Cu-water based nanofluid with heat transfer phenomenon is reported for scraped-surface heat exchanger. The flow is initiated due to motion of lower wall of the channel and axial pressure gradient. The flow is modelled with aid of low Reynolds number and lubrication approximation theory. Exact analytical expressions are gathered for axial velocity, and stream functions for various stations of scraped-surface heat exchanger. Physical phenomenon of electro osmotic parameter are investigated on velocity profile, velocity distribution and pressure rise at edge of the blades. It is reported that electro-osmotic parameter mainly works as dragging force, it can be used to control the flow. This controlling mechanism may be helpful in mixing different materials in scraped-surface heat exchanger. Pressure rise at edge of the blades mainly rises below the blades with electro-osmotic, whereas, this profiles is suppressed for region above the blades and between the blades.

Flow in groovy curved channels with thin gap

A pressure-driven viscous flow through groovy curved channels of small width compared to the groove wavelength is studied. The Reynolds number is assumed to be very small, such that the flow is dominated by the viscous and the pressure-gradient forces. The effects of the channel geometry on the inertial free flow are analyzed. Two distinct flow directions are considered: (i) flow transverse to the grooves and (ii) flow longitudinal to the grooves. The velocities for both flow directions are obtained, and their distributions are found to be significantly affected by the grooves and channel curvature. The axial pressure gradient for the transverse flow is examined as a function of the amplitude and the phase difference. The results further indicate that the flow rate can be increased by the grooves for longitudinal flow, irrespective of the phase difference, unlike transverse flow This is because the latter is more affected by grooves for the same radius of curvature and phase difference.

Self-sustaining critical layer/shear layer interaction in annular Poiseuille–Couette flow at high Reynolds number

The nonlinear stability of annular Poiseuille–Couette flow through a cylindrical annulus subjected to axisymmetric and helical disturbances is analysed theoretically at asymptotically large Reynolds number R based on the radius of the outer cylinder and the constant axial pressure gradient applied. The inner cylinder moves with a prescribed positive or negative velocity in the axial direction. A distinguished scaling for the disturbance size Δ = O ( R −4/9 ) is identified at which the jump in vorticity across the fully nonlinear critical layer is in tune with that induced across a near-wall shear layer. The disturbance propagates at close to the velocity of the inner cylinder and possesses a wavelength comparable to the radius of the outer cylinder. The dynamics of the critical layer, shear layer and the Stokes layer adjacent to the stationary wall are discussed in detail. In the majority of the pipe, the disturbance is governed predominantly by inviscid dynamics with the pressure perturbation satisfying a form of Rayleigh’s equation. For a radius ratio δ in the range 0 < δ < 1 and a positive sliding velocity V , a numerical solution of the Rayleigh equation exists for sliding velocities in the range 0 < V < 1 − δ 2 + 2 δ 2 ln δ , whereas if V < 0, solutions exist for 1 − δ 2 + 2ln δ < V < 0. The amplitude equations for both these situations are derived analytically, and we further find that the corresponding asymptotic structures break down when the maximum value of the basic flow becomes located at the inner and outer walls, respectively.