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.

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.

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.

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.

Impact of radiation,melting,and chemical reaction on magnetohydrodynamics nanoparticle aggregation flow across parallel plates

The heat transfer between two corresponding plates,disks,and concentric pipes has many applications,including water cleansing and lubrication.Furthermore,TiO_(2)-water-based nanofluids are used widely because it is useful for operating and controlling the temperature,especially in photovoltaic technology and solar panels.Motivated by these applications,the current study is based on the nanoparticle aggregation effect on magnetohydrodynamics(MHD)flow via rotating parallel plates with the chemical reaction.To achieve maximum heat transportation,the Bruggeman model is used to adapt the Maxwell model.Also,melting and thermal radiation effects are considered in the modeling to discuss heat transport.The Runge-Kutta-Fehlberg 4th−5th order method is used to attain numerical solutions.The main focus of this study is to see the thermodynamic behavior considering several aspects of nanoparticle aggregation.The heat transfer rate between the parallel plates is enhanced by improving the thermophoresis,radiation,and Brownian motion parameters.The rise in Schmidt number and chemical reaction rate parameter decreases the concentration distribution.This study will be helpful in enhancing the thermal efficiency of photovoltaic technology in solar plates,water purifying,thermal management of electronic devices,designing effective cooling systems,and other sustainable technologies.

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.

Fault Location Method and Simulation Analysis of Parallel Compensating Capacitors

At present, the operational parallel compensating capacitors can only through the protection action for the information, so we can‘t location the fault capacitor. In order to obtain every parallel capacitor running status information and meanwhile according to internal structure and the operation mode of film capacitor, this paper established the physical model on the single capacitor and the capacitors and simulated different forms of capacitor fault model and calculated currents changes which flow through the capacitor in every group. According to the above situation, we established fault criterion matrix of capacitors. The simulation results show that the fault criterion matrix can reflect capacitor running state information accurately, and it positioned fault capacitor effectively.

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.

Nonlinear vibration analysis of a circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method

In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.

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.

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.

Influence of Filling Ratio and Working Fluid Thermal Properties on Starting up and Heat Transferring Performance of Closed Loop Plate Oscillating Heat Pipe with Parallel Channels

Using ethanol or acetone as the working fluid, the performance of starting up and heat transfer of closed-loop plate oscillating heat pipe with parallel channels(POHP-PC) were experimentally investigated by varying filling ratio, inclination, working fluids and heating power. The performance of the tested pulsating heat pipe was mainly evaluated by thermal resistance and wall temperature. Heating copper block and cold water bath were adopted in the experimental investigations. It was found that oscillating heat pipe with filling ratio of 50% started up earlier than that with 70% when heating input was 159.4 W, however, it has similar starting up performance with filling ratio of 50% as compared to 70% on the condition of heat input of 205.4 W. And heat pipe with filling ratio of 10% could not start up but directly transit to dry burning. A reasonable filling ratio range of 35%-70% was needed in order to achieve better performance, and there are different optimal filling ratios with different heating inputs- the more heating input, the higher optimal filling ratio, and vice versa. However, the dry burning appeared easily with low filling ratio, especially at very low filling ratio, such as 10%. And higher filling ratio, such as 70%, resulted in higher heat transfer( dry burning) limit. With filling ratio of 70% and inclination of 75°, oscillating heat pipe with acetone started up with heating input of just 24 W, but for ethanol, it needed to be achieved 68 W, Furthermore, the start time with acetone was similar as compared to that with ethanol. For steady operating state, the heating input with acetone was about 80 W, but it transited to dry burning state when heating input was greater than 160 W. However, for ethanol, the heating input was in vicinity of 160 W. Furthermore, thermal resistance with acetone was lower than that with ethanol at the same heating input of 120 W.

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

By introducing the functional theory into the calculation of electric double layer （EDL） interaction, the interaction energies of two parallel plates were calculated respectively at low, moderate, and high potentials. Compared with the results of two existing methods, Debye-Hückel and Langmuir methods, which are applicable just to the critical potentials and perform poorly in the intermediate potential, the functional approach not only has much simpler expression of the EDL interaction energy, but also performs well in the entire range of potentials.

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.

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.

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.

Rotating Capacitor and a Transient Electric Network

This paper presents a rotating parallel-plate capacitor;one of the plates is assumed to turn about the common vertical axis through the centers of the square plates. Viewing the problem from a purely geometrical point of view, we evaluate the overlapping area of the plates as a function of the rotated angle. We then envision the rotation as being a mechanical continuous process. We consider two different rotation mechanisms: a uniform rotation with a constant angular velocity and, a rotation with a constant angular acceleration—we then evaluate the overlapping area as a continuous function of time. From the electrostatic point of view, the time-dependent overlapping area of the plates implies a time-dependent capacitor. Such a variable, a time-dependent capacitor has never been reported in literature. We insert this capacitor into a series with a resistor, forming a RC circuit. We analyze the characteristics of charging and discharging scenarios on two different parallel tracks. On the first track we drive the circuit with a DC power sup-ply. We study the implications of the rotation modes. We compare the response of each case to the corresponding tradi-tional constant capacitor of an equivalent RC circuit;the quantified results are intuitively just. On the second track, we drive the circuit with an AC source. Similar to the analysis of the first track, we generate the relevant electrical characteristics. In the latter case, we also analyze the sensitivity of the response of the circuit with respect to the fre-quency of the source. The analyses of the circuits encounter nontrivial differential equations. We utilize Mathematica [1] to solve these equations.

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.

PARALLEL FINITE ELEMENT ANALYSIS OF HIGH FREQUENCY VIBRATIONS OF QUARTZ CRYSTAL RESONATORS ON LINUX CLUSTER

Quartz crystal resonators are typical piezoelectric acoustic wave devices for frequency control applications with mechanical vibration frequency at the radio-frequency （RF） range. Precise analyses of the vibration and deformation are generally required in the resonator design and improvement process. The considerations include the presence of electrodes, mountings, bias fields such as temperature, initial stresses, and acceleration. Naturally, the finite element method is the only effective tool for such a coupled problem with multi-physics nature. The main challenge is the extremely large size of resulted linear equations. For this reason, we have been employing the Mindlin plate equations to reduce the computational difficulty. In addition, we have to utilize the parallel computing techniques on Linux clusters, which are widely available for academic and industrial applications nowadays, to improve the computing efficiency. The general principle of our research is to use open source software components and public domain technology to reduce cost for developers and users on a Linux cluster. We start with a mesh generator specifically for quartz crystal resonators of rectangular and circular types, and the Mindlin plate equations are implemented for the finite element analysis. Computing techniques like parallel processing, sparse matrix handling, and the latest eigenvalue extraction package are integrated into the program. It is clear from our computation that the combination of these algorithms and methods on a cluster can meet the memory requirement and reduce computing time significantly.