Microparallel Channel Research Articles

An exact solution for the entropy base flow of electroosmotic magneto-nanofluid through microparallel channel

An exact solution of steady state, electroosmotic, transient magnetohydrodynamic (MHD) flow, and heat transfer of a viscous and incompressible electrically conducting nanofluid consists of water and Cu metal, through a microparallel channel under the combined effect of pressure and vertically acting magnetic field is found. An exact solution is calculated through Laplace transform using the software of Mathematica to find the steady velocity and temperature field depending on many dimensionless parameters. The electromagnetic couple effect, the volumetric generation of heat caused by the Joule heating effect, and viscous dissipation are considered to analyze the thermally fully formed heat flow problem based on the steady part of the velocity field. The exact result of the temperature field is obtained by taking the uniform boundary heat flux. The significant parameter of heat flow known as the Nusselt number, depending on the height of the microtube, is defined. At last, the entropy generation of MHD temperature flow is analyzed. The interpretation of variations that occurred in internal and external entropy generations is given and consequences are explained.

Electroosmotic flow of two-layer fluid containing Oldroyd-B fluid with fractional derivative in a rotating microparallel channel

Electroosmotic flow of two-layer fluid containing Oldroyd-B fluid with fractional derivative in a rotating microparallel channel

Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials

By using the Caputo–Fabrizio time fractional derivative, unsteady flows of an incompressible viscous through a circular tube are developed. Flows are generated due to the combination of electroosmotic, pressure and magnetic forces. The derived fractional momentum equation incorporating the electromagnetic body force resulting from the electric double layer (EDL) field was solved using the Laplace transform technique, Riemann-sum approximation method, and the Stehfest’s algorithm. The solution obtained is validated by assenting comparisons between the Riemann-sum approximation method and Stehfest’s algorithm. Based upon the velocity field solution, the energy equation is analyzed by taking the viscous dissipation, thermal radiative, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect into account. Numerical simulations and graphical illustrations were carried out using the software package Mathcad. The results highlights that, fractional models of fluid-flow and heat transfer with fractional derivatives bring significant differences compared to the ordinary model. The variations of fluid velocity, fluid temperature, skin friction and Nusselt number with related parameters are interpreted and the results are discussed.

Streaming potential analysis on the hydrodynamic transport of pressure-driven flow through a rotational microchannel

In this study, the streaming potential and electrokinetic energy conversion efficiency are discussed under the low zeta potential approximation through a microparallel channel with consideration of rotational effect. By solving Poisson-Boltzmann equation and modified Navier–Stokes equation, the analytical expressions of the streaming potential and electrokinetic energy conversion efficiency in the electrolyte solution are obtained. Combining with the numerical calculation, the influences of the dimensionless electrokinetic width K and the rotational angular velocity ω on streaming potential and the electrokinetic energy conversion efficiency are discussed. The results show that the streaming potential fields decrease both in mainstream and secondary directions with the electrokinetic width K, it decreases with the non-dimensional rotational angular velocity in the mainstream direction and it shows a first increasing then decreasing trend in the secondary flow direction. In addition, the influences of related non-dimensional parameters, including electrokinetic width, wall electric potential and rotational angular velocity, on the electrokinetic energy conversion efficiency are also discussed in detail. The rotating effect can enhance conversion efficiency comparing to the case of no rotation. The increase of wall electric potential gives rise to an augment in electrokinetic energy conversion efficiency. These theoretical results make sense to the energy harvesting in the rotating microfluidic systems.

Rotating electroosmotic flow of two-layer fluids through a microparallel channel

In this study, rotating electroosmotic flow of two immiscible fluids in a microparallel channel is investigated. The electric double layer (EDL) potential distribution is considered by using linear Poisson–Boltzmann (P-B) equation. Based upon the analytical charge density distribution, an analytical solution of flow velocity can be obtained by solving the modified Navier–Stokes (N-S) equation in the rotating frame. Besides, the equilibrium condition of stress, including shear stress and Maxwell stress, is taken into account as boundary conditions at the interface to analyze the distribution of the two-layer fluids velocity. It is found that, due to the rotational effect of the microchannel, the Coriolis force can generate a (secondary) transverse flow in horizontal direction perpendicular to the mainstream direction and the velocity amplitude of two-layer fluids has a reduced flow along the mainstream direction. In addition, the results indicate that double fluid velocity distribution is strongly influenced by several non-dimensional parameters, such as the dielectric constant ratio ε, density ratio ρ, viscosity ratio μ of the two layer fluids, rotating angular velocity ω, interface zeta potential difference Δφ*, interface charge density jump Q, the normalized thickness of two layer Newtonian fluids h1*, h2* and electrokinetic width K1, K2. Smaller μ and larger ε, Δφ* lead to larger velocity amplitude for lower fluid (noted as fluid II), but an opposite trend can be found for upper fluid (namely fluid I). The increase of Q or decrease of ρ leads to the increases of velocity amplitude for both fluid I and fluid II. Furthermore, interestingly, we observe that the mainstream speed at the interface does not depend on the interface zeta potential difference Δφ*, the dielectric constant ratio ε and electrokinetic width K2 of fluid II when the depths of h1* and h2* are identical.

Entropy generation of two-layer magnetohydrodynamic electroosmotic flow through microparallel channels

The entropy generation analysis of two-layer magnetohydrodynamic electroosmotic flow through a microparallel channel is performed in this study. The two immiscible fluid flows are both driven by a combination of electroosmotic force, pressure gradient and electromagnetic force. Under the framework of Debye-Hückel linearization approximation as well as the assumption of thermally fully developed and the condition of constant wall heat flux, the distributions of velocity and temperature are analytically derived and they are utilized to compute the entropy generation rate. The effects of fluid physical parameter ratios on the distributions of two-layer fluid velocity and temperature are firstly discussed. Then the local and total entropy generation rates are investigated for different magnetic field parameter (Ha) and the viscous dissipation parameter (Br) under the appropriate fluid physical parameter ratios. The results show that the entropy generation rate strongly depends on the velocity and temperature fields and the local entropy generation reveals a decreasing trend form the microchannel wall towards the fluid interface for both bottom and upper layer fluid. The present endeavor can be utilized to design the efficient thermal micro-equipment.

Rotating electromagnetohydrodynamic flow of power-law fluids through a microparallel channel

In this study, rotating electromagnetohydrodynamic (EMHD) flow of power-law fluid through a narrow microchannel is investigated. The flow is actuated by the Coriolis force raised from the rotation of the microchannel and the Lorentz force induced by the interaction between electric and magnetic fields. The modified Navier-Stokes equations in the rotating frame are discretized by the finite difference method and solved through Crank-Nicolson implicit scheme under the appropriate initial and boundary conditions. Results of the present analysis are compared with existing literature for special case when the behavior index n of power-law fluid is equal to unit (Newtonian fluid). Very well agreements are obtained and the validity of the present numerical method is confirmed. The influences of the fluid behavior index n, the Hartmann number Ha and rotating Reynolds number ReΩ on the EMHD velocity distributions are discussed. The results show the velocity of the power-law fluid depends strongly on these flow parameters. Due to the existence of the uniform electric and magnetic fields, the critical Hartmann number can also be obtained for the power-law fluid. In addition, for the small Ha, a depression only appears in mainflow direction at the central part of the microchannel and the dilatant fluid (n>1) is easily affected by the rotation effect comparing to the pseudoplastic fluid (n<1). Regarding the evolution of centerline velocity of the power-law fluids with ReΩ, an auspicious phenomenon is that there exists a cross-over point for different values of the behavior index n. The present results can be utilized as an initial blue-print for the developing exquisite and efficient electromagnetic devices for applications involving flow control or species separation.

Combined electromagnetohydrodynamic flow in a microparallel channel with slightly corrugated walls

In this work a perturbation method is introduced to study the effect of wall roughness on the combined electromagnetohydrodynamic flow in a microparallel channel with slightly corrugated walls under the Debye–Hückel approximation. The driving force is the sum of the electro-osmotic and Lorentz forces. The wall corrugations are described by periodic sinusoidal waves with small amplitudes compared to the channel height. The perturbation solutions of velocity and electric potential are obtained. The results show that the velocity and potential distributions are significantly disturbed by the wall roughness. The mean velocity can be enhanced at long-wavelength corrugations when the phase difference between the wall corrugations is near π. The enhancement of the mean velocity increases with S which represents the strength of the electric field in the x-direction. The decreasing effect of wall roughness increases with the wavenumber and decreases with the phase difference and the normalized reciprocal thickness of the electric double layer. The phase difference of wall roughness becomes unimportant when the wavenumber or Hartmann number is larger than 3.

The flow of micropolar fluids through a microparallel corrugated channel

The flow of micropolar fluids through a microparallel channel with corrugated walls is performed in this paper. The corrugations of the two walls are described as periodic sinusoidal waves with small amplitude and phase difference \( \theta\). The flow generated by the constant pressure gradient is assumed to be steady and unidirectional. Approximate analytical solutions of velocity, vorticity of micro-rotation and volume flow rate are obtained by perturbation techniques. The effects of the corrugation on the flow are graphically analyzed by using numerical computation. The dependences of velocity, vorticity of micro-rotation and leading-order perturbations to the mean velocity of micropolar fluids on the Reynolds number Re, the phase difference \( \theta\) of the two corrugated walls and couple stress parameter s0 are explained graphically.

Electroosmotic flow through a microparallel channel with 3D wall roughness.

In this paper, a perturbation method is introduced to study the EOF in a microparallel channel with 3D wall roughness. The corrugations of the two walls are periodic sinusoidal waves of small amplitude in two directions either in phase or half-period out of phase. Based on linearized Poisson-Boltzmann equation, Laplace equation, and the Navier-Stokes equations, the perturbation solutions of velocity, electrical potential, and volume flow rate are obtained. By using numerical computation, the influences of the wall corrugations on the mean velocity are analyzed. The variations of electrical potential, velocity profile, mean velocity, and their dependences on the wave number α and β of wall corrugations in two directions, the nondimensional electrokinetic width K, and the zeta potential ratio between the lower wall and the upper wall ς are analyzed graphically.

Transient MHD heat transfer and entropy generation in a microparallel channel combined with pressure and electroosmotic effects

By using the method of Laplace transform, analytical investigations are performed for combined unsteady electroosmotic, pressure driven and magnetohydrodynamic (MHD) flow of an electrically conducting, incompressible and viscous fluid through a slit parallel plate microchannel under the action of a vertical magnetic field. The velocity profiles for different time and their dependence on several non-dimensional parameters are explained graphically. Based upon the velocity field of steady part, the thermally fully developed heat transfer problem are analyzed by taking the viscous dissipation, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect into account. The exact solution of temperature field is derived subjected to constant wall heat flux condition. The dependence of several dimensionless parameters on temperature and the Nusselt number Nu based on channel height is presented graphically. Finally, the entropy generation analysis of MHD heat transfer is performed. The variations of local and global entropy generations with related parameters are interpreted and the results are discussed.

Electromagnetohydrodynamic (EMHD) flow between two transversely wavy microparallel plates.

In this paper, 2D electromagnetohydrodynamic (EMHD) flow in a microparallel channel with slightly transverse corrugated walls is investigated using perturbation method. The corrugations of the two walls are presented by periodic sinusoidal waves with small amplitudes. The perturbation solutions of the stream function and a relation between flow rate and roughness are obtained. It is shown that the flow rate always decreases due to the wall corrugations irrespective of the phase difference. For prescribed Hartmann number and wave number of the wavy walls, the flow resistance increases as the phase difference between the wall corrugations increases. The effect of corrugation on the flow rate decreases with Hartmann number. With the increase of wave number, the effects of corrugations on the flow rate increase. The phase difference of wall corrugations becomes unimportant when the wave number is greater than 4. The obtained results for the flow rates as a function of the applied current are in qualitative agreement with the existing experimental results.

Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls

In this paper a perturbation method is introduced to study the electromagnetohydrodynamic (EMHD) flow in a microparallel channel with slightly corrugated walls. The corrugations of the two walls are periodic sinusoidal waves of small amplitude either in phase or half-period out of phase, and the perturbation solutions of velocity and volume flow rate are obtained. Using numerical computation the effects of the corrugations on the flow are graphically analysed. The results show that the influence of corrugation on the flow decreases with Hartmann number. The phase difference of wall corrugations becomes unimportant when the wavenumber is greater than 3 or when the Hartmann number is greater than 4. With the increase in wavenumber, the decreasing effects of corrugations on the flow increase. When the wavenumber is smaller than the threshold wavenumber (it is a function of Hartmann number) and the wall corrugations are half-period out of phase, the corrugations can enhance the mean velocity of EMHD flow. However, the mean velocity is always decreased when the corrugations are in phase.

Transient AC Electro-Osmotic Flow of Generalized Maxwell Fluids through Microchannels

In this paper, we represent analytical solutions of transient velocity for electroosmotic flow (EOF) of generalized Maxwell fluids through both micro-parallel channel and micro-tube using the method of Laplace transform. We solve the problem including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation and generalized Maxwell constitutive equation. By numerical calculation, the results show that the EOF velocity is greatly depends on oscillating Reynolds number and normalized relaxation time.

Transient electro-osmotic flow of generalized Maxwell fluids through a microchannel

Non-Newtonian fluids such as blood, colloids, and cell suspensions are often manipulated in microfluidic devices and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. This paper represents an analytical solution of transient velocity for electroosmotic flow of generalized Maxwell fluids through both a micro-parallel channel and a microtube, using the method of Laplace transform. The solution involves analytically solving the linearlized Poisson–Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influence of normalized relaxation time on transient EOF velocity is investigated for different parametric values.