Non-parallel Plates Research Articles

Equilibrium States of a Liquid Bridge between Flexible Sheets.

We study the equilibrium states of a drop between flexible sheets clamped on both ends. Revisiting first the case of parallel sheets, we find multiple equilibria, which we classify in a parameter space. In solution branching diagrams, we identify hysteresis cycles and folds indicating abrupt transitions, yet not necessarily leading to channel collapse. Between nonparallel sheets, a drop can stay in equilibrium away from the ends even when the liquid is not totally wetting, which is impossible between nonparallel rigid plates. We also show that nonparallel sheets can delay or prevent collapse in comparison to straight channels, suggesting thus a mechanism that protects slender structures inside microdevices from damage by surface tension.

Duan Rach approach solution of MHD flow of ternary hybrid Casson magnetized nanofluid in converging/diverging geometry with velocity slip effects

This study explores the impact of ternary hybrid nanofluid and velocity slip on the Non-Newtonian fluid flow between two nonparallel plates. Additional influence of an applied magnetic field is considered with Casson fluid (Blood) as a base fluid. Both analytic and numerical techniques are employed to comprehensively analyze the system’s behavior under these combined effects. The governing partial differential equations (PDEs) governing continuity and momentum are simplified into a system of ordinary differential equations (ODEs) through similarity transformations. To obtain an explicit series solution for the resulting problem, we employ the Duan Rach approach (DRA). Subsequently, we conduct a thorough analysis of the solution’s convergence to ensure its reliability and accuracy. The same problem is also solved by using the Runge-Kutta-Fehlberg 4th–5th order approach featuring shooting technique and an excellent agreement is observed between the two sets of results. A comparison was made between the results obtained from this investigation in particular cases and the results obtained via the HAM-based Mathematica package for validation. Influence of various parameters of practical importance on the velocity and temperature profiles is studied and portrayed graphically. Values of skin friction coefficient are tabulated by assigning different values to various emerging parameters. It is found that the velocity slip parameter has a positive value in a converging channel, it implies that there is a slip between the fluid and the channel wall, and the slip velocity is directed in the same direction as the flow. Hence velocity increases. Also, results obtained reveal that for positive value of β + velocity gets high in converging case and lower velocity can be seen in diverging geometry. Same behavior is seen for β − .

Study on MHD hybrid nanofluid flow with heat transfer in a stretchable converging/diverging channels embedded in a porous medium with uncertain volume fraction

This study considers a hybrid nanofluid flow in a non-parallel plate embedded in permeable stretchable convergent and divergent channels. It investigates the impact of the magnetic field and heat transmission on the velocity and temperature profiles of the hybrid nanofluid flow. Here, the walls of the stationary channels are considered to be allowed to stretch or shrink, and the hybrid nanofluids are Cu-Ag, with water as the base fluid. The nanoparticle volume fraction of hybrid nanofluid is considered an uncertain parameter, represented with a triangular fuzzy number ranging from 0.0 − 0.04 . A novel double parametric homotopy approach is used to study the impacts of the relevant parameters on the velocity and temperature profiles and validate the obtained result by comparing it with previously published literature in the crisp case without the porous medium. Finally, the fuzzy velocity and temperature profiles at distinct channel locations are graphically illustrated, accompanied by numerical representations of velocity and temperature bounds at various positions along the stretchable convergent/divergent channels.

On the solution of MHD Jeffery–Hamel problem involving flow between two nonparallel plates with a blood flow application

AbstractThe Jeffery–Hamel flow phenomenon appears in a variety of real‐world applications involving the flow of two nonparallel plates. BY using a similarity transformation derived from the equation of continuity, partial differential equations determining flow characteristics are translated into nonlinear ordinary differential equations. The problem involves the flow of a specific type of fluid, namely, an incompressible and electrically conducting fluid, between two nonparallel plates. The flow is assumed to be steady, two‐dimensional, and subject to certain boundary conditions. Specifically, the plates are impermeable, and the fluid adheres to a no‐slip condition, resulting in zero fluid velocity at the plates' surfaces. Moreover, the problem incorporates the effects of magnetic fields and pressure fluctuations, making it highly applicable to scenarios, such as blood flow through arteries in the human body, which can be modeled as a special case of the magnetohydrodynamic (MHD) Jeffery–Hamel problem referred to as the (MHD) blood pressure equation. This work compares two numerical approaches for solving the MHDs Jeffery–Hamel problem: B‐spline and Bernstein polynomial collocation. The given approaches are used to discretize and transform the equation into a system of algebraic equations. Matrix algebra techniques are then used to solve the resultant system. A complete error analysis and convergence rates for different grid sizes are derived for both methods and are used to compare the accuracy and efficiency of the two approaches. Both approaches produce correct solutions, according to the numerical findings, although the Bernstein polynomial collocation method is more efficient and accurate than the B‐spline collocation.

Capillary condensation between nonparallel walls.

We study the condensation of fluids confined by a pair of nonparallel plates of finite height H. We show that such a system experiences two types of condensation, termed single and double pinning, which can be characterized by one (single-pinning) or two (double-pinning) edge contact angles describing the shape of menisci pinned at the system edges. For both types of capillary condensation, we formulate the Kelvin-like equationand determine the conditions under which the given type of condensation occurs. We construct the global phase diagram revealing a reentrant phenomenon pertinent to the change of the capillary condensation type upon varying the inclination of the walls. Asymptotic properties of the system are discussed and a link with related phase phenomena in different systems is made. Finally, we show that the change from a single- to a double-pinned state is a continuous transition, the character of which depends on the wetting properties of the walls.

Structural design and multi-objective optimization of a novel asymmetric magnetorheological damper

The MRD with continuously adjustable damping, small compression, and large extension for asymmetric output may improve all-terrain vehicle impact resistance and vibration reduction performance in a variety of conditions. A novel conical flow channel asymmetric MRD (CFC-MRD) is proposed to solve the structure complexity stroke sacrifice, and lack of failure protection concerns in currently studied asymmetric MRD structures. In the design, the non-parallel plate magnetic circuit characteristics of CFC-MRD are investigated, including theoretical analysis and finite element modeling, and the correctness of the model is proved by testing. Considerations in multi-objective optimization include special performance imposing extra restrictions, and making the work more complicated and prone to local optima. To address this, the Nelder–Mead approach is utilized, which decreases the complexity of the optimization model while simultaneously managing performance conflicts. And a collaborative optimization strategy employing Comsol and Matlab tools is applied to improve optimization efficiency. The greatest difference between theoretical optimized values and real values is less than 6.77% in the experiments, showing the efficiency of the CFC-MRD structure design and optimization process.

Theoretical switch model of novel asymmetric magnetorheological damper for shock and vibration application

This study proposed a novel asymmetric conical flow channel magnetorheological damper (CFC-MRD) for all-terrain vehicles (ATVs) to handle complex excitations with coexisting shocks and vibrations. CFC-MRD produces adjustable damping forces by utilizing magnetically controlled properties and achieves asymmetric force output (moderate compression force and strong extension force) with conical flow channels. This design could effectively absorb and dissipate energy. The paper first illustrates the structure and asymmetric principle of CFC-MRD. Then, the mechanism of asymmetric force generation in a non-parallel flat plate is derived, and utilizes the hydrodynamic theory to derive the pressure difference of Bingham fluid between the non-parallel plates. Considering the coexistence of vibration and shock, the study proposes a theoretical switch model that distinguishes between low and high velocity states based on the Reynolds number. Finally, the validity of the model is verified by experiments, and the results show that the CFC-MRD achieves the desired asymmetric force output. The asymmetric force ratio rises with higher excitation speed and drops with increased drive current. At a speed of 1 m s−1 without any applied current, the maximum asymmetric force reaches 1.21. The small peak error, averaging only 2.57%, between experimental and theoretical results affirms the accuracy of the proposed switch model.

The study of capillarity phenomena by means of ImageJ software

"Capillarity phenomena appear due to different molecular forces acting between fluid molecules located at the interface with either another fluid or a solid. The macroscopic description of the phenomenon can be done in terms of surface tension. In this paper, we determined the surface tension coefficient of aqueous solution of potassium permanganate by means of Jurin's law and also made diameter measurements and capillary ascents on images by using ImageJ software. Furthermore, we studied the capillary phenomena between two parallel and non- parallel plates. In the case of non-parallel plates, employing a special plugin of the ImageJ software, we determined the equation of the rectangular hyperbola drawn by the surface of liquid rising between plates. These experiments can be performed at elementary level and, additionally, used as a stimulus to discover more advanced topics."

Design optical surface as the measurement datum in measuring gear tooth flank by symmetrical laser interferometer

Laser interferometry is a promising method to measure the form deviation of gear tooth flanks. The lack of measurement datum is the bottleneck problem of measuring a gear tooth flank by laser interferometry. Manufacturing a physical reference gear tooth flank as the measurement datum has many drawbacks which restrain the application prospect of measuring gear by laser interferometry. Optical surfaces are more mature to manufacture and have much higher processing accuracy compared with the physical reference tooth flank. Thus, we design and use an optical surface as the measurement datum. First, we invent a symmetrical oblique incidence laser interferometer (SOILI) to reduce the interference fringe’s density and enhance the tractability of interferograms. Second, we propose a design method for calculating the measured tooth flank’s similar optical surface. Lastly, we propose the nonparallel plate model which is a general form of the parallel plate model and can be used to calculate the situations where the normal directions of the measured surface and the reference surface are different. Experimental results verify that an optical surface can be designed and used as the measurement datum. Furthermore, this research provides some references for the measurement datum in the relevant comparative measurements processes by laser interferometry.

Hysteretic Behavior of Capillary Bridges between Flat Plates.

We studied the evolution of capillary bridges between nominally flat plates undergoing multiple cycles of compression and stretching in experiments and simulations. We varied the distance between the plates in small increments to study the full evolution of the bridge shape. Experiments show that contact angle hysteresis determines the shape of the bridge. In sliding drops, hysteresis can be modeled using a contact angle-dependent resistive force F̃R applied at the contact line. We developed a model that accurately captures the evolution of the bridge shape by combining F̃R and constrained energy minimization. Unlike previous work, this allows for both complete and partial contact line pinning. We also explored the effect of using nonparallel plates. The asymmetry in the bridge shape causes the movement of the center of mass of the bridge and can be explained by contact angle hysteresis. We find that even a slight misalignment between the flat plates can have a measurable effect.

Study on the parameters of detached dual splitter plates and comparison with single plate for VIV suppression

In the actual marine engineering environment, vortex-induced vibration will affect the safety of cylindrical structures. Rigid splitter plates have become one of the suitable VIV suppression solutions due to their simple structure and low maintenance costs. Therefore, on the basis of numerical simulation, this paper analyses the influence of the gap between parallel and non-parallel double splitter plates and the arrangement angle of non-parallel double splitter plates on the VIV suppression effect at a fixed flow rate. In addition, the VIV suppression effect of the single and dual splitter plates with the same parameter combination is evaluated under the condition of multi-flow velocity. It is found that the parallel dual splitter plate cannot provide good VIV suppression, especially when the gap exceeds the cylinder diameter, the suppression effect begins to deteriorate. However, on the basis of a certain gap between the plates, the dual splitter plate with arrangement angle is more effective than the single splitter plate in suppressing the transverse vibration of the cylinder. Therefore, when using dual splitter plates for VIV suppression, the parallel dual splitter plates should be avoided. When a better transverse vibration suppression effect is required, the arrangement angle can be appropriately changed.

Modeling and numerical handling of viscous dissipation in second order viscoelastic fluid flow in a nonparallel channel

This work gives an insight into the viscous effects of a viscoelastic fluid on the flow and heat transfer when it is put to flow between two nonparallel plates via some source/sink. Modeling of the problem is presented in detail with focus on the viscous dissipation effect. Afterwards, the problem is solved numerically by Keller Box method and bvp4c routine using MATLAB. The comparative analysis of the two techniques has been drawn on the basis of numerical values of Nusselt number. Alongside this, a comprehensive detail of the impact of pertinent parameters on the flow and temperature profiles have been given. The numerical results give an insight about the fluid characteristics like velocity, temperature, heat transfer and skin friction with variations in pertinent physical parameters.

New Analytical Study of Heat Transfer Analysis of Jeffery–Hamel Nanofluid Flow Problem with Porous Medium

In this study, a perturbation iteration scheme (PIS), is used to investigate the flow and heat transfer of a nanofluid through a convergent or divergent channel in a porous medium for the Jeffrey Hamel flow problem. Under the influence of the magnetic field, the nanofluid continuously flows through the channel. Modeling of the motion of different nanofluids is done with the aid of momentum and energy equations. The effect of some variables such as opening channel angle, Reynolds number, Darcy number, Hartmann number, Prandtl number, and Eckert number, on nanofluidic flows through non-parallel plates has been discussed. It has been observed that as velocity rises, fluid viscosity increases with a higher Reynolds number. The internal friction also decreases as the Darcy number rises because of an increase in flow and an increase in heat transfer. Additionally, when the results of the remaining variables were examined and their effects on the velocity and temperature profiles were compared with those of related studies in the literature, a satisfactory level of agreement was found. This is clear from the tables and drawings mentioned in this manuscript, and it also shows that this approach gives us a good study for examining the Jeffrey Hamel problem.

Modeling and analysis of dual modules cantilever-based electrostatic energy harvester with stoppers

Based on the cantilever beam, this paper proposes and designs a novel electret-based electrostatic energy harvester (e-EEH) with dual modules: module I is a capacitor of nonparallel plate electrodes; module II is a multi-electrode array capacitor. Two stoppers are presented in concern with reliability by limiting the motion of proof mass to prevent capacitor breakdown and pull-in. Meanwhile the stoppers serve as a functional element to realize broadband harvesting. Considering the bending of the cantilever beam, the expression of the module Ⅰ capacitance is analytically derived as a function of the deflection. Conformal transformation is applied to obtain the expression of the module Ⅱ capacitance, simultaneously considering the change of distance and overlap area between movable and fixed electrodes. According to Hamilton's principle and Kirchhoff's circuit law, the electromechanical coupling nonlinear dynamics equations of the proposed energy harvesters are established. The output performance of the energy harvester is obtained and analyzed by numerical calculation. The results show that the double-model electrostatic energy harvester can output high power in low- frequency broadband.

Squeeze film flow of viscoplastic Bingham fluid between non-parallel plates

Squeeze film flow of a viscoplastic Bingham fluid between non-parallel plates has been analysed. It is assumed that the force applied to the plates is known, therefore, their velocity must be found, and the film thickness decreases then as time proceeds. Moreover, for non-parallel plates, the position along the plates at which flow reverses direction is found as part of the solution. In the Newtonian limit, the thickness of the gap between the plates in the parallel system never quite reaches zero at any finite time, while for the non-parallel case a finite time can be obtained when the plates touch one another at a point. In squeeze flow of a viscoplastic Bingham fluid between parallel and non-parallel plates, under a fixed applied force, a final steady film thickness can sometimes be reached. This final thickness turns out to be sensitive not just to the plate tilt angle but also to the so called Oldroyd number which is defined as the ratio between yield stress and imposed stress. Nevertheless for squeeze film flow of Bingham viscoplastic fluid between non-parallel plates, the results show that other cases exist in which the lubrication force cannot always balance the applied force, leading to the plates approaching and touching at the narrowest end of the gap. Moreover torques that develop within the system have been analysed. • Squeeze flow of fluid between non-parallel plates is considered. • Fluid is considered as Bingham viscoplastic. • In some cases, plates stop at finite height; in other cases, plates touch. • Which case is realised depends on tilt angle and Oldroyd number. • Torque in Bingham fluid is lower than in Newtonian.

The electrical magnetohydrodynamic (MHD) and shape factor impacts in a mixture fluid suspended by hybrid nanoparticles between non-parallel plates

Abstract In this research work, we introduce the influences of the shape of nanoparticles and joule heating in the hydromagnetic flow of hybrid nanofluids between non-parallel plates. A mixture base fluid (H2O (50%)-C2H6O2 (50%)), a hybrid nanofluid containing hybrid nanoparticles (graphene oxide-molybdenum disulfide, GO-MoS2) as nanoparticles, is considered. The non-linear governing equations are reduced into ordinary-differential equations (ODEs) by similarity transformations. The non-linear ordinary-differential equation (ODE) is solved numerically utilizing 4th–5th order Runge-Kutta-Fehlberg (RKF-45) with a shooting method and analytically using the homotopy analysis method (HAM). The effect of the rarefaction parameter, Reynolds number, channel angle, Hartmann number, electric field parameter, and the shape of nanoparticles on fluid velocity and skin friction are discussed and presented in a graphical form. Also, the theoretical results and the effectiveness of the homotopy analysis method (HAM) are confirmed by numerical tests and presented graphically coupled with detailed discussions.

Heat transfer analysis of CNTs‐water nanofluid flow between nonparallel plates: Approximate solutions

AbstractApproximate solutions are given to investigate the problem of heat transfer and flow of a nanofluid between two nonparallel plates. Two different types of carbon nanotube (CNT) nanoparticles, namely functionalized single‐walled carbon nanotubes and functionalized multi‐walled carbon nanotubes are considered with water as the base fluid. The chemical functionalization is attributed to the attachment of the covalent bond of functional groups onto carbon nanotubes. Using the appropriate similarity variables, the model partial differential equations are transformed into ordinary differential equations and tackled analytically via the homotopy perturbation method. Comparison of the obtained results is carried out with those obtained by the previously published in the literature as well as the Runge–Kutta–Fehlberg method and an excellent agreement is achieved. The effects of various emerging parameters on nanofluid velocity, temperature, skin friction coefficient, and Nusselt number are illustrated graphically and comprehensively discussed.

Thermal, frictional and exergetic analysis of non-parallel configurations for plate heat exchangers

Parallel configuration is the main common and conventional structure of the plate heat exchangers. However, this paper focuses on non-parallel configuration for these types of heat exchangers and clarifies whether these configurations are more thermally efficient compared to the parallel plates. Besides, frictional and exergetic behavior of non-parallel structures are investigated as well. As shown in the graphical abstract, eight configurations are possible for non-parallel structures all of which are comprehensively studied in this research using a validated 3-D numerical simulation. The results show that the non-parallel plates provide higher Nusselt number and thermal performance factor compared to the common parallel plates. In the same value of inlet mass flow rate, case “e” in which hot fluid moves though the converge channel and cold fluid moves through the divergent channel obtains the maximum Nu number. Obtained thermal performance factors higher than unity show the positive role of non-parallel structures with consideration of both Nusselt number and friction factor. Generally, it is concluded that non-parallel structures can be considered as an efficient method to augment the efficiency of plate heat exchangers. Many other parameters in term of second law of thermodynamics are studied for all structures as well in this study.

New modified decomposition method (DRMA) for solving MHD viscoelastic fluid flow: comparative study

In this article, the magnetohydrodynamic (MHD) of Jeffery-Hamel flow (JHF) of viscoelastic fluid in converging/diverging channels is investigated, the viscoelastic fluids and when the stationary rigid nonparallel plates are permitted to stretch (shrink) are taken into account. The solution of the flow model is solved numerically by using the Runge–Kutta-Fehlberg 4th–5th order method (RKF-45) based on shooting technique and analytically by the Duan-Rach modified Adomian decomposition method (DRMA). It is found that the incrementation of Reynolds number and channel-half angle in convergent flow leads to an increase of velocity distribution and means that backflow is excluded; however, a reversal behaviour is observed in diverging flow. The skin friction coefficient decreases with the increase of both of the and , while it increases with the augment of the Hartman number . The present results were compared to justify the efficiency and the higher accuracy of the used DRMA.

Investigation of nanofluid conveying porous medium through non-parallel plates using the Akbari Ganji method

This paper presents the study on the Jeffery Hamel nanofluid flow and heat transfer through non-parallel channel taking into account radiation effect. The fluid with porous medium flowing through the non-parallel channel is formulated utilizing momentum and energy equations. Since the model obtained are nonlinear, higher order systems of equations, the Akbari Ganji novel approximate method is adopted in this paper. As reported in the graphical representation of the result, it is depicted that the porous medium limits flow due to increased dynamic viscosity leading to pressure drop while the radiation parameter enhances heat loss through the non-parallel plates. This evidently leads to energy loss. The Akbari–Ganji method is used in this study to investigate the parametric behavior of rheological parameters on the flow and heat transfer owing to its high accuracy. Results obtained in this study compared against analytical and numerical solution obtained in literature shows satisfactory conclusion. Therefore, results from this paper may be useful in advancing studies of nanofluid with porous medium.