UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

A New Idea of Fractal-Fractional Derivative with Power Law Kernel for Free Convection Heat Transfer in a Channel Flow between Two Static Upright Parallel Plates

Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.

Influence of Hartmann Number on Convective Flow of Maxwell Fluid between Two Hot Parallel Plates through Porous Medium Subject to Arbitrary Shear Stress at the Boundary

Natural convection flow of unsteady Maxwell fluid with the effects of constant magnetic force in the course of a porous media is investigated in this research work. Fluid motion between a channel of parallel plates is tempted by time dependent shear stress applied on one plate. The governing partial differential equations of a model under consideration are transformed into ordinary differential equations by Laplace transform method and then solved for temperature and velocity fields. The obtained results for temperature fields are expressed in terms of complementary error function. The influences of involved parameters likes Hartmann number, Grashf number, Prandlt number and porosity parameter, on temperature and velocity profiles are shown graphically. There is no such result regarding Maxwell fluid in the existing literature.

Study on Interaction Between Two Parallel Plates with Iteration Method in Functional Theory

由介绍功能的理论进电的双层(EDL ) 的计算相互作用，二个平行盘子的相互作用精力在低、中等、高的潜力分别地是计算的。与二存在方法的结果相比， Debye-H 湲獥？

Mathematical Analysis of Unsteady MHD Blood Flow through Parallel Plate Channel with Heat Source

In the present study, a mathematical model of unsteady blood flow through parallel plate channel under the action of an applied constant transverse magnetic field is proposed. The model is subjected to heat source. Analytical expressions are obtained by choosing the axial velocity;temperature distribution and the normal velocity of the blood depend on y and t only to convert the system of partial differential equations into system of ordinary differential equations under the conditions defined in our model. The model has been analyzed to find the effects of various parameters such as, Hartmann number, heat source parameter and Prandtl number on the axial velocity, temperature distribution and the normal velocity. The numerical solutions of axial velocity, temperature distributions and normal velocity are shown graphically for better understanding of the problem. Hence, the present mathematical model gives a simple form of axial velocity, temperature distribution and normal velocity of the blood flow so that it will help not only people working in the field of Physiological fluid dynamics but also to the medical practitioners.

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.

Converging Parallel Plate Flow Chambers for Studies on the Effect of the Spatial Gradient of Wall Shear Stress on Endothelial Cells

Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.

Hall Current Effects on Unsteady MHD Flow in a Rotating Parallel Plate Channel Bound-ed by Porous Bed on the Lower Half—Darcy Lapwood Model

We discussed the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate. The flow in the clean fluid region is governed by Navier-Stoke’s equations while in the porous bed the equations are based on Darcy-Lapwood model. The exact solutions of velocity in the clean fluid and the porous medium consist of steady state and transient state. The time required for the transient state to decay is evaluated in detail and ultimate quasi-steady state solution has been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters. The shear stresses on the boundaries and the mass flux are also obtained analytically and their behaviour is computationally discussed.

Hall Effects on Unsteady MHD Three Dimensional Flow through a Porous Medium in a Rotating Parallel Plate Channel with Effect of Inclined Magnetic Field

In this paper, we make an initial value investigation of the unsteady flow of incompressible viscous fluid between two rigid non-conducting rotating parallel plates bounded by a porous medium under the influence of a uniform magnetic field of strength H0 inclined at an angle of inclination α with normal to the boundaries taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate while the lower plate is at rest. The flow in the porous medium is governed by the Brinkman’s equations. The exact solution of the velocity in the porous medium consists of steady state and transient state. The time required for the transient state to decay is evaluated in detail and the ultimate quasi-steady state solution has been derived analytically. Its behaviour is computationally discussed with reference to the various governing parameters. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed.

Effect of End Shape on Flow and Heat Transfer Characteristics of Two Parallel Plates

Flow around a pair of flat plates is a basic hydrodynamics problem.In this paper,the flow and heat transfer characteristics of two parallel plates with different edge shapes are numerically calculated.Under different inclined angles,the influence of chamfered and rounded structures with different sizes at the end-edge on unsteady flow and heat transfer characteristics of two parallel plates are analyzed.It is found that the instability and unsteadiness of flow decrease with the increase of end-edge size,and the non-uniformity of wake velocity of both rounded and chamfered plates decreases gradually.The non-uniformity of wake temperature increases firstly and then decreases at a small inclined angle,and the amplitude becomes the largest when S_(rou)(S_(cha))=3,while it basically keeps monotonically increasing at a large inclined angle.Moreover,the global heat transfer performance of the flat plate is obviously affected by the end-edge modification,especially the chamfered structure.With the increase of chamfered size,the global Nusselt number basically shows the decreasing trend.This study provides a theoretical basis for the application of plate-shape structure in engineering fields.

Temperature Bias Drift Phase-Based Compensation for a MEMS Accelerometer with Stiffness-Tuning Double-Sided Parallel Plate Capacitors

This paper reports an approach of in-operation temperature bias drift compensation based on phase-based calibration for a stiffness-tunable MEMS accelerometer with double-sided parallel plate(DSPP)capacitors.The temperature drifts of the components of the accelerometer are characterized,and analytical models are built on the basis of the measured drift results.Results reveal that the temperature drift of the acceleration output bias is dominated by the sensitive mechanical stiffness.An out-of-bandwidth AC stimulus signal is introduced to excite the accelerometer,and the interference with the acceleration measurement is minimized.The demodulated phase of the excited response exhibits a monotonic relationship with the effective stiffness of the accelerometer.Through the proposed online compensation approach,the temperature drift of the effective stiffness can be detected by the demodulated phase and compensated in real time by adjusting the stiffness-tuning voltage of DSPP capacitors.The temperature drift coefficient(TDC)of the accelerometer is reduced from 0.54 to 0.29 mg/℃,and the Allan variance bias instability of about 2.8μg is not adversely affected.Meanwhile,the pull-in resulting from the temperature drift of the effective stiffness can be prevented.TDC can be further reduced to 0.04 mg/℃through an additional offline calibration based on the demodulated carrier phase representing the temperature drift of the readout circuit.

Multipacting saturation in parallel plate and micro-pulse electron gun

A novel parallel plate model is proposed that divides the electron cloud into three parts at saturation, and it is studied in detail using both an analytical approach and particle-in-cell （PIC） code simulations. As one part of the electron cloud, ribbons modes are suggested by tracking the trajectory of individual particles, and the aim of this mode form is to simplify the progress of the multipacting effect in the parallel plate so as to be eliminated by optimizing RF parameters. The micro-pulse electron gun （MPG） has demonstrated the potential to address the need for high peak and average current electron beams, hence studying the multipacting in MPG is essential. On the basis of studying multipacting in the parallel plate, it is clear that increasing the cavity voltage is of interest in yielding high quality beams in the gun.

Performance Analysis of Thermoacoustic Refrigerator of 10 W Cooling Power Made up of Poly-Vinyl-Chloride for Different Parallel Plate Stacks by Using Helium as a Working Fluid

Refrigerants are usually provided in the conventional refrigeration system although the refrigerants produce Chlorofluorocarbons(CFCs)and Hydro-chlorofluorocarbons(HCFCs),which are hazardous to the environment.However,these disadvantages can be overcome by using air or inert gas in the thermoacoustic refrigeration system.In the present experimental work,helium is used as a working gas with an operating pressure range of 0.2 MPa to 1.0 MPa in order to study the performance of thermoacoustic refrigerator(TAR)which is fabricated using Poly-Vinyl-Chloride(PVC).The parallel plate stacks with different porosity ratios have been considered to study the performance of TAR.The temperature difference between the hot and cold heat exchanger and acoustic dynamic pressure were recorded by using Bruel and Kjaer data acquisition system under different operating conditions.The effect of different operating parameters such as operating frequency(200 Hz to 600 Hz),cooling load(2 W to 10 W)and drive ratio(0.6%to 1.6%)have also been considered to study the performance of TAR.The TAR also modeled in DeltaEC software and the results are compared with the experimental outcomes and found to be in good agreement.The experimental results show that-2.1℃is the lowest temperature measured at cold heat exchanger by achieving the highest temperature difference of about 32.9℃.An improvement is around 36%as compared to that of previous experiments that used aluminium TAR.The highest Coefficient of Performance(COP)and the Relative Coefficient of Performance(COPR)are found to be 2.024 and 0.217,respectively.

Predicting wall drag coefficient and settling velocity of particle in parallel plates filled with Newtonian fluids

The hindrance of boundary to particle transport exists widely in various industrial applications.In this study,the wall drag force of parallel plates on settling particles was revealed through settling experiment.High-speed camera was used to record and analyze the settling process of particles in parallel plates that are filled with Newtonian fluids.A total of 600 experiments were carried out,involving the range of relative diameter and particle Reynolds number of 0.01-0.95 and 0.004-14.30,respectively.The wall drag coefficient was defined to quantitatively analyze the wall drag force of the parallel plates.The influence of relative diameter,particle properties,rheological properties,and the settling dynamic process on the wall drag coefficient was revealed,and the wall drag coefficient model with mean relative error of 5.90% was established.Furthermore,an explicit settling velocity model with mean relative error of 8.96% for the particle in parallel plates was developed by introducing a dimensionless variable independent of settling velocity,the Archimedes number.Finally,a calculation example was provided to clarify the using process of the explicit model.This research is expected to provide guidance for optimizing water hydraulic fracturing in the oil and gas industry.

OPTIMIZATION OF TRANSIENT FEEDING TO PARALLEL-PLATE TRANSMISSION LINES FROM COAXIAL LINE

The transient feeding to parallel-plate transmission lines from coaxial line is optimized by using the Finite-Difference Time-Domain (FDTD) method and a simple FDTD feed model. Observing the reflected voltages, this letter presents the optimal feeding position and ratio of width to height for a given input impedance of the coaxial line.

ON ANALYSIS OF THE STEADY FLOW IN AN IRRECTANGULARPARALLEL-PLATE FLOW CHAMBER

The parallel-plate flow chamber (PPFC), of which the height is far smaller than its own length and width, is one of the main apparatus for the in vitro study of the mechanical behaviors of cultured cells at the bottom of PPFC undergoing shear stress. The PPFC of which the upper and lower plates are rectangular is usually used by research workers, and the flow field in this kind of PPFC (except for the regions near the entrance and exit) is uniform([1]), so only the effect the shear stress with one value has on cultured cells can be observed during each experiment. A kind of PPFC of which the upper and lower plates are not rectangular is proposed in this paper. The distributions of the velocities inside and the shear stresses at the bottom of the chamber are given by analyzing the flow field of the steady flow in the PPFC. The results show that the mechanical behaviors of cultured cells undergoing the shear stresses with various values may be simultaneously observed by the use of this kind of irrectangular PPFC. The theoretical and experimental results obtained by Ultrasonic Doppler Technique show good agreement.

Unsteady time-dependent incompressible Newtonian fluid flow between two parallel plates by homotopy analysis method(HAM),homotopy perturbation method(HPM)and collocation method(CM)

Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation.The powerful analytical methods called collocation method(CM),the homotopy perturbation method(HPM),and the homotopy analysis method(HAM)have been used to solve nonlinear differential equations.It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem.Also,velocity fields have been computed and shown graphically for various values of physical parameters.The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field.

Experiment investigation on visualization and operating characteristics of closed loop plate oscillating heat pipe with parallel channels

Using ethanol or acetone as the working fluid, visualization of oscillations in steady state was observed visually by high-speed cameras, and temperature oscillating and heat transfer characteristics of closed-loop plate oscillating heat pipe with parallel channels(POHP-PC) were experimentally investigated by varying liquid filled ratios(50%, 70%, 85%), section scales(1 mm×1 mm and 1 mm×1.5 mm), inclination angles, working fluids and heating inputs. It was found that during operating there was mixed flow consisting of plug flow and annular flow in channels of oscillating heat pipe at steady-state. There was an equilibrium position for working fluid of condenser during oscillating, and periodic oscillations occurred up and down in the vicinity of equilibrium position. With heat input increasing, equilibrium position rose slowly as a result of vapor pressure of evaporation.Evaporation temperature oscillating amplitude possessed a trend of small-large-small and frequency trend was of small-large during steady-state. It may be generally concluded that temperature, whether evaporator or condenser, fluctuated sharply or rose continuously when oscillating heat pipe coming to dry burning state. Simultaneously, it was found that temperature difference of cooling water possibly dropped with heat input rising during dry burning state. Thermal resistance of No. 2 with acetone was lower than that of No. 1 during experiments, but No. 2 achieving heat transfer limit was earlier than No. 1. However, with ethanol, thermal resistance of No. 1 and No. 2 were similar with the heating input less than 110-120 W and filling ratios of 50% and 70%. And with filling ratio of 85%, heating transfer performance of No. 2 was better compared to No. 1 during all the experiments.

MULTI-MODE NETWORK ANALYSIS FOR DISCONTINUITIES IN PARALLEL-PLATE WAVEGUIDES PARTIALLY FILLED WITH MULTI CHIRAL RODS

The reflection and transmission characteristics of the guided modes in parallel-plate waveguides partially filled with one or multi chiral rods have been investigated by a method, which combines the multi- mode network theory with a rigorous mode matching procedure. The formulas of the reflection and transmis- sion coefficient matrix are derived. The numerical results for different cases are presented and have indicated that the chirality parameters and the geometrical dimensions of the chiral rods have significant influence on the reflection and transmission characteristics of the guided modes.

THE PARALLEL CONFOCAL DETECTING SYSTEM USING OPTICAL FIBER PLATE

Objective Focusing on the problem such as slow scanning speed, complex system design and low light efficiency, a new parallel confocal 3D profile detecting method based on optical fiber technology, which realizes whole-field confocal detecting, is proposed. Methods The optical fiber plate generates an 2D point light source array, which splits one light beam into N2 subbeams and act the role of pinholes as point source and point detecting to filter the stray light and reflect light. By introducing the construction and working principle of the multi-beam 3D detecting system, the feasibility is investigated. Results Experiment result indicates that the optical fiber technology is applicable in parallel confocal detecting. Conclusion The equipment needn't mechanical rotation. The measuring parameters that influence the detecting can easily be adapted to satisfy different requirments of measurement. Compared with the conventional confocal method, the parallel confocal detecting system using optical fiber plate is simple in the mechanism, the measuring field is larger and the speed is faster.