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.

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.

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.

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.

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.

Numerical Fluid Flow Modelling in Multiple Fractured Porous Reservoirs

This paper compares the fluid flow phenomena occurring within a fractured reservoir for three different fracture models using computational fluid dynamics.The effect of the fracture-matrix interface condition is studied on the pressure and velocity distribution.The fracture models were compared based on the variation in pressure and permeability conditions.The model was developed for isotropic and anisotropic permeability conditions.The results suggest that the fracture aperture can have a drastic effect on fluid flow.The porous fracture-matrix interface condition produces more realistic transport of fluids.By increasing the permeability in the isotropic porous matrix,the pressure drop was significantly higher in both the fracture and reservoir region.Under anisotropic conditions in the 3D fractured reservoir,the effect of the higher longitudinal permeability was found to lower the pressure in the fractured reservoir.Depending on the properties of the fractured reservoir,this study can enhance the understanding of fracture-matrix fluid interaction and provide a method for production optimisation.

Investigation of Heat Transfer Augmentation between the Ribbed Plates via Taguchi Approach and Computational Fluid Dynamics

Heat transfer and turbulent flow characteristics between the ribbed plates have been numerically studied in the present paper.The ribs with the rectangular cross-section have been placed on the top and the bottom plates of the duct,symmetrically.It is assumed that the fluid at 300 K has entered the system while the walls kept at 400 K.All numerical analyses have been performed by k-ωShear Stress Transport(SST)turbulence model for Re=10000,15000 and 20000.For the fixed rib width,the dimensionless height and the dimensionless spacing have been respectively varied as 0.1≤h’≤0.3 and 0.5≤S’≤1,and the results have been compared with the ones of the smooth plate.Even though there are twenty-seven cases obtained as a result of parametric combinations,the number of various cases has been reduced from twenty-seven to only nine different variations by applying the Taguchi method.Furthermore,the effects of all the considered parameters on the heat transfer and flow characteristics have been determined in terms of the influence degree.The optimum parameters for Nusselt number and pressure loss have been ascertained individually.What is more,the almost exact values for Nusselt number and pressure loss have also been attained by the confirmation test having an error percentage of 6%.The most dominant factor has been determined as the rib height due to its effect on both heat transfer and flow characteristics.Similarly,with respect to the numerical results,increasing the rib height,the rib spacing and Reynolds number has separately increased Nusselt number.Nevertheless,symmetrical flow structure has been disturbed as a result of ascending the rib height as clearly seen for h’=0.3 from the charts.In the meantime,pressure loss has been augmented owing to the increment of the geometrical parameters and also Reynolds number.h’=0.1 with S’=0.5 at Re=10000,h’=0.2 with S’=0.5 at Re=15000 and h’=0.1 with S’=0.75 at Re=15000 can be suggested for the heat transfer enhancement since the pressure loss of the system is tolerated.

Modeling natural convection heat transfer from perforated plates

Staggered pattern perforations are introduced to isolated isothermal plates,vertical parallel isothermal plates,and vertical rectangular isothermal fins under natural convection conditions.The performance of perforations was evaluated theoretically based on existing correlations by considering effects of ratios of open area,inclined angles,and other geometric parameters.It was found that staggered pattern perforations can increase the total heat transfer rate for isolated isothermal plates and vertical parallel plates,with low ratios of plate height to wall-to-wall spacing(H/s),by a factor of 1.07 to 1.21,while only by a factor of 1.03 to 1.07 for vertical rectangular isothermal fins,and the magnitude of enhancement is proportional to the ratio of open area.However,staggered pattern perforations are detrimental to heat transfer enhancement of vertical parallel plates with large H/s ratios.

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.

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.

THE PROPERTIES OF A SINGLE POLYMER CHAIN IN SOLVENT CONFINED IN A SLIT: A MOLECULAR DYNAMICS SIMULATION

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h （h is the distance between two plates）, until a basin occurs, and a universal h/（Rg）o dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain＇s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.

Irreversibility analysis of unsteady couette flow with variable viscosity

This paper investigates numerically the inherent irreversibility in unsteady generalized Couette flow between two parallel plates with variable viscosity. The nonlinear governing equations are derived from the Navier-Stokes equations and solved numerically using a semi-discretization finite difference method together with the Runge-Kutta-Fehlberg integration scheme. The profiles of velocity and the temperature obtained are used to compute the entropy generation number, Bejan number, skin friction and Nusselt number. The effects of embedded parameters on entire flow structure are presented graphically and discussed quantitatively.