Oscillating Boundary Conditions Research Articles

Nonlinear dynamics of dissipative water conveying SWCNT/MWCNT/Ferro nanofluid subject to radiation: Thermal analysis by linear slope regression

Carbon nanotubes have gained significant attention due to their unique properties like small dimensions, high thermal conductivity, and unique architecture. These nanotubes have enormous potential in various fields such as nanomedicine, mechanical compound materials, sensor devices, bio-sensors, and many other applications. The present study investigates the impact of adding nanoparticles such as iron oxide (Fe3O4), single-walled carbon nanotubes (SWCNT), and multi-walled carbon nanotubes (MWCNT) on magnetohydrodynamics (MHD) oscillatory water-based flow over a porous medium. The aim is to examine the effect of heat and mass transfer rate and radiative viscous dissipation that interacts with Fe3O4 nanoparticles and carbon nanotubes. The governing equations of the dynamic nanofluid systems are transformed into a set of coupled nonlinear partial differential equations through suitable dimensionless transformations and further converted into ordinary differential equations by taking appropriate solutions for oscillatory-type nanofluid flow. The homotopy perturbation method is applied to solve the governing equations with oscillatory boundary conditions and the solution is also compared with the numerical solver bvp4c. The rate of increase in the temperature and Heat Transfer are computed by the linear slope regression method and results are computed for nanoparticles SWCNT, MWCNT, and Ferro. Also, Skin friction and rate of heat transfer are computed and compared for the nanoparticles with varying Peclet and Eckert numbers. The velocity profile and temperature profile of SWCNT/MWCNT/Ferro nanofluids are being compared. The heat transfer rate is observed to be high for Ferro nanoparticles compared to SWCNT and MWCNT.

High Order Multiscale Methods for Advection-Diffusion Equation with Highly Oscillatory Boundary Condition

High Order Multiscale Methods for Advection-Diffusion Equation with Highly Oscillatory Boundary Condition

Mathematical modeling of pulsations in the drillingfluid

Purpose. To improve the efficiency of cleaning wells from drilled rock by using a pulsating flow of drilling fluid. to study the effect of cuttings concentration and distance from the pulse source on the parameters of its oscillations. The methods. Based on the analysis of the peculiarities of the well flushing process, the possibility of using an uneven flow of drilling mud created by fluid pressure fluctuations at the bottom of the well mathematical modeling of fluctuations in the two-phase environment of the flow of drilling fluid with drilled rock was carried out. In order to construct a mathematical model of oscillatory vibrations, the initial and boundary conditions for solving the homogeneous wave equation of the third order are set. The solution of this equation is realized using the Fourier method. Based on the results of the analytical calculations, a program in the JavaScript environment was developed to study the effect of cuttings concentration and distance from the pulse source on the vibration parameters. Findings. Using the developed program, the dependence of the change in the intrinsic vibration displacement of a two-phase medium on time was investigated when the cuttings concentration varies from 0 to 13 % in the drilling fluid and the distance from the pulse source varies from 1 to 1000 m. It was found that the vibration displacement in time is a sinusoidal curve with a certain period. It was found that the pulsation frequency decreases in hyperbolic dependence with distance from the pulse source due to attenuation in a two-phase medium. It was found that pulsations propagate effectively at a distance of up to 300 m from the pulse source. The effect of the cuttings concentration in the drilling fluid on the pulsation frequency is investigated. The originality. A mathematical model of the process of rock particles removal through the annular space of the well by a pulsating flow of drilling fluid is created. Practical implementation. Software has been developed to assess the effect of cuttings concentration and distance from the pulse source on the oscillation parameters, which will allow to evaluate and improve the process of well cleaning with a pulsating flow of drilling fluid.

An unconditionally stable third order scheme for mixed convection flow between parallel plates with oscillatory boundary conditions

AbstractThis work proposes an unconditionally stable third‐order multistep technique for time‐dependent partial differential equations. Its unconditional stability is proved by employing von Neumann stability analysis, and constructed Matlab code is another solid proof of the existence of the such scheme. The scheme is constructed on three consecutive time levels, and a compact fourth‐order scheme is considered for spatial discretization. The convergence conditions are found when applied to the system of parabolic equations. The scheme is tested on two examples of flow between parallel plates. The mathematical model of heat and mass transfer of flow between parallel plates under the effects of viscous dissipation, thermal radiations, and chemical reaction is given and solved by the proposed scheme. The impact of some parameters, including radiation and reaction rate parameters, on velocity, temperature, and concentration profiles is also illustrated by graphs. The proposed scheme is also compared with the existing scheme, providing faster convergence than an existing one. The fundamental benefit of the proposed scheme is that it can give a compact fourth‐order solution to parabolic equations.

Numerical Investigation on EOR in Porous Media by Cyclic Water Injection with Vibration Frequency

Water injection with an oscillatory pressure boundary is a promising technology, which can achieve a more economical and environment-friendly EOR (enhanced oil recovery). However, due to the unclear critical injection frequency, its oil production performance has been unstable and is far from reaching the optimal level. Here, a numerical model is established for oil recovery by the water injection with the oscillatory boundary condition to find out the critical frequency for the optimal EOR. The correlations between the water injection frequency and the EOR level at diverse oil–water surface tensions and oil viscosities are integrated into the model. Our numerical model reveals that an optimal EOR of roughly 10% is achieved at the critical water injection frequency compared with water injection without an oscillatory boundary. The EOR mechanism is revealed showing that upon water injection with the optimum frequency, the formation of the preferential pathways is inhibited and the pressure transmits to the wall sides to displace the oil. Moreover, it is indicated that the required critical frequency increases with higher surface tension and larger oil viscosity. In addition, the difference between the residual oil saturation at the optimal frequency increases with the increase in surface tension compared with water injection without an oscillatory boundary. Last but not least, it is elucidated that at a constant injection frequency, a higher EOR is achieved when the water–oil surface tension is lower but the oil viscosity is larger. Our work promises economic, eco-friendly and controllable enhanced oil recovery.

A Dimensional optimization study on cyclone performance under the oscillating boundary condition

In this study, the effect of changing the diameter of the vortex finder, cone and hydraulic inlet diameter of the cyclone under oscillating flow conditions is compared to under uniform flow. In using cyclones as an inlet air filter for the internal combustion engine, the cyclone flow cannot be considered ideally uniform, and flow oscillations must be applied to the boundaries. Also, optimizing the dimensions of the cyclone can provide the necessary space for other uses in the engine space. Numerical solution validation has been performed and seven cyclone models have been created. Then, the effect of geometry variation on the flow field is investigated by examining the frequency and power of active vortices in the vortex finder, cylinder and cone zones. Also, the cyclone performance parameters, including Euler number and efficiency, have been investigated for different models, and correlations have been proposed to estimate them under non-uniform flow. Multi-objective optimization is performed using the genetic algorithm for introducing the most optimal cyclone geometry. Under non-uniform flow conditions, increasing the vortex finder and cone diameter by 50% and decreasing the hydraulic inlet diameter by 40% reduce the Euler's number by 52 to 62%.

Quasi-analytical study of dynamic performance of the thermocline heat storage system under time-varying inlet flow and temperature environment

The dynamic thermal performance of single-tank thermocline (STTC) thermal energy storage (TES) system under oscillating boundary conditions (BCs) during cloud cover or start-up period is critical to the safety and efficiency of the whole concentrating solar power (CSP) plant. In this study, the approximate analytical solution of the STTC TES system under oscillating velocity and temperature BCs are derived from the one dimensional-two phase (1D-2P) models, which can be applied in arbitrary realistic BCs with Fourier decomposition method. After model validation with dynamic experimental data, the effects of typical sinusoidal oscillating parameters on packed bed transport phenomena and TES efficiency were investigated. It is found both of the oscillating inlet velocity and temperature lead to degradation of thermal stratification, such as outlet temperature fluctuation, while it also causes enhanced heat transfer effect and increased charging/discharging cut-off efficiency. Cut-off efficiency increases with amplitude of oscillating inlet velocity or oscillating inlet temperature, while for oscillating frequency there is optimum value. On that basis, the general optimum equation of cut-off efficiency and oscillating frequency is proposed, and the relative error is smaller than 1.0% when outlet temperature is larger than 0.011 for the discharging process with oscillating inlet velocity BC and smaller than 3.2% for oscillating inlet temperature BC. Moreover, the thermocline region movement velocity increases with inlet velocity for oscillating inlet velocity BC and decreases with oscillating frequency for oscillating inlet temperature BC.

MHD flow, radiation heat and mass transfer of fractional Burgers' fluid in porous medium with chemical reaction

Non-Newtonian fluids such as asphalt are widely used in engineering field, but their application will also cause environmental pollution. This paper investigates the MHD flow of this kind of non-Newtonian fluid in porous media by using fractional Burgers' model. The effects of first-order chemical reaction, radiation effects and periodic oscillating boundary condition on fluid flow, heat and mass transfer are considered. The governing equations including a multi-term time fractional derivative are obtained by using the modified Darcy's law, fractional Fourier's law and fractional Fick's law. A convergent and stable L-algorithm, is established for governing equations. The influences of model parameters on the velocity, temperature and concentration distributions are analyzed. Numerical simulation results indicate that fractional derivative α and Darcy number Da have significant effect on velocity distribution. The momentum boundary layer becomes thinner remarkably with fractional derivative α. While the influence of Darcy number Da on the velocity performs conversely.

Reaction-Diffusion Dynamics of pH Oscillators in Oscillatory Forced Open Spatial Reactors.

Studying the effect of coupling and forcing of oscillators is a significant area of interest within nonlinear dynamics and has provided evidence of many interesting phenomena, such as synchronization, beating, oscillatory death, and phase resetting. Many studies have also reported along this line in reaction–diffusion systems, which are preferably explored experimentally by using open reactors. These reactors consist of one or two homogeneous (well-stirred) tanks, which provide the boundary conditions for a spatially distributed part. The spatiotemporal dynamics of this configuration in the presence of temporal oscillations in the homogeneous part has not been systematically investigated. This paper aims to explore numerically the effect of time-periodic boundary conditions on the dynamics of open reactors provided by autonomous and forced oscillations in the well-stirred part. A simple model of pH oscillators can produce various phenomena under these conditions, for example, superposition and modulation of spatiotemporal oscillations and forced bursting. The autonomous oscillatory boundary conditions can be generated by the same kinetic instabilities that result in spatiotemporal oscillations in the spatially distributed part. The forced oscillations are induced by sinusoidal modulation on the inflow concentration of the activator in the tank. The simulations confirmed that this type of forcing is more effective when the modulation period is longer than the residence time of the well-stirred part. The use of time-periodic boundary conditions may open a new perspective in the control and design of spatiotemporal phenomena in open one-side-fed and two-side-fed reactors.

Damped Vibration Response of An Axially Moving Wire Subject to An Oscillating Boundary Condition and the Application to Slurry Wiresaws

AbstractThis paper presents the analysis of a new class of differential continuum system with a solution of traveling waves containing coupled spatial and temporal variables. Herein, we derive the analytical solution of the damped vibration response of a longitudinally moving wire with damping, subject to an oscillating boundary condition. The vibration response is the outcome of combining four traveling waves, induced by a wave initiating from the oscillating boundary, and traveling between the two boundaries. The four different traveling waves are the independent bases of the vibration responses that span the solution space of vibration of such continuum system. The combination, or the interference, of these traveling waves in the undamped condition produces nodal points in the vibration response, which can be formulated through the analytical solution. The impacts of wire speed, oscillating frequency at the boundary and damping factors on the vibration response are investigated. Furthermore, the vibration induced by the oscillating motion of the boundary has a profound impact on the effectiveness of slicing ingots with rocking motion of oscillating wire guides in wiresaw manufacturing processes.

Experimental Study of the Impact of a Vibrating Wire on Free Abrasive Machining as Correlated to the Modeling of Vibration Subject to an Oscillating Boundary Condition

Abstract In this paper, we study experimentally the impact of a vibrating wire on the free abrasive machining (FAM) process in removing material from the surface of brittle materials, such as silicon. An experimental setup was designed to study the FAM process on silicon substrate surface by using a slurry-fed wire with a periodic excitation. An analytical solution of a wire moving axially, subject to an oscillating boundary condition with damping from abrasive slurry, was derived based on the partial differential equation of motion. Experiments were conducted on the apparatus using a wire with an oscillating boundary. It was found that the amplitudes of vibration were larger at the side of the oscillatory boundary, which caused more FAM interaction near the edge of the oscillatory boundary with larger material removal that was measured and validated. Furthermore, experiments were conducted to elucidate the effectiveness of brittle material removal using FAM with abrasive grits: (i) under dry condition, (ii) with water, and (iii) with abrasive slurry. Experimental results showed that the vibration of wire resulted in plastic deformation on the surface of silicon wafer. The abrasive grits in slurry driven by a vibrating wire generated material removal through observable grooves and fractures on the surface of silicon due to FAM in just a few minutes. The grooves from FAM process is an outcome of brittle machining through fracture formation and concatenation, generated by the indentation of abrasive grits on the silicon surface.

Novel insights into the computational techniques in unsteady MHD second‐grade fluid dynamics with oscillatory boundary conditions

AbstractThis study presents mechanisms for the investigation of an unsteady magnetohydrodynamic second‐grade fluid flow between two periodically oscillating plates. The flow characterization is given in three forms, that is, Couette flow, Poiseuille flow, and a combination flow of both of them. A mathematical system is generated to design the problems, which are solved in an analytical way with two novel procedures, namely Adomian decomposition method (ADM) and optimal homotopy asymptotic method (OHAM). The numerical comparison, absolute errors, and residuals of OHAM and ADM solutions are evaluated. Results obtained from these two methods are studied comparatively in the form of numbers and graphs. A good agreement between the respective data is obtained. The influences of flow parameters like frequency parameter, non‐Newtonian fluid parameter, magnetic field parameter, pressure gradient parameter, and time variable on velocity have been analyzed.

Time-dependent rationally extended Pöschl–Teller potential and some of its properties

We examine time-dependent Schrodinger equation with oscillating boundary condition. More specifically, we use separation of variable technique to construct time-dependent rationally extended Poschl–Teller potential (whose solutions are given by in terms of $$X_1$$ Jacobi exceptional orthogonal polynomials) and its supersymmetric partner, namely the Poschl–Teller potential. We have obtained exact solutions of the Schrodinger equation with the above-mentioned potentials subjected to some boundary conditions of the oscillating type. A number of physical quantities like the average energy, probability density, expectation values, etc., have also been computed for both the systems and compared with each other.

Design, optimization and numerical simulation of a MicroFlow sensor in the realistic model of human aorta

Among all arterial diseases, aneurysm and atherosclerosis are of great importance. In these diseases the cross-section area of the artery and therefore the blood flow velocity changes. Therefore, it is a good idea to use a micro flow sensor for measuring the blood flow velocity to diagnosing these diseases. In this study, design, geometric optimization and numerical simulation of a hotfilm microsensor in the realistic model of human's aorta are investigated. A normal aorta geometry is extracted from CT Angiography images, and after applying oscillating boundary conditions on the inlet and outlet arteries, blood flow parameters are investigated by computational fluid dynamics (CFD) simulation. After designing the microsensor, the effects of its location in different aorta regions on the blood flow characteristics are numerically investigated. The results show that in the presence of microsensor, streamlines patterns almost remain unchanged while the maximum blood flow velocity in the aorta cross section where the microsensor is located, increases up to 10%. It is also found that the secondary flow weakens when the microsensor enters the artery causing a reduction in velocity measurement error. Furthermore, because of the presence of a catheter, the pressure drop increases up to 768 Pa. Results show that less than 30% of the arterial cross-sectional area where the microsensor is located, senses an increase in temperature.

Natural convection flow of a fluid using Atangana and Baleanu fractional model

A modified fractional model for the magnetohydrodynamic (MHD) flow of a fluid is developed utilizing Atangana–Baleanu fractional derivative (ABFD). Natural convection and wall oscillation instigate the flow over a vertical plate positioned in a porous medium. The partial differential equations (PDEs) are transmuted to ordinary differential equations (ODEs). The Laplace transform method with its inversion is employed to accomplish the exact solutions of momentum and heat equations. The final solution is expressed in terms of gamma function, modified Bessel function, and Mittag-Leffler function. The previous definitions Caputo fractional and Riemann–Liouville are rarely used by the researchers now due to their limitations. The newly introduced ABFD has got significance nowadays due to its nonlocal and nonsingular kernel. This work focuses on the oscillating boundary conditions for the viscous model in terms of ABFD. The influence of involved parameters is interpreted through plots. The velocity profile is an increasing function of fractional parameter and jumps for a higher Grashof number due to buoyancy push. Furthermore, the Atangana–Baleanu (AB) model is compared with the ordinary derivative model for limiting case and analyzed in detail. It is noted that the ordinary fluid flows faster compared to the fractional fluid.

The effects of oscillating boundary conditions on thermal ignition

We investigate the effect that oscillating ambient temperatures have on the ignition times of supercritical stockpiles. Large stockpiles are exposed to seasonal and diurnal temperature variation. We analyse the effects of seasonal temperature variation. When considering ignition within a year of construction, stockpiles built in spring ignited with a lower critical parameter than those built at other times. Consequently, seasonal temperature variation needs to be accounted for when predicting stockpile ignition times.

Explicit finite difference solution for contaminant transport problems with constant and oscillating boundary conditions

For constant and oscillating boundary conditions, the 1-D advection-diffusion equation with constant coefficients, which describes a contaminant flow, is solved by the explicit finite difference method in a semi-infinite medium. It is shown how far the periodicity of the oscillating boundary carries on until diminishing to below appreciable levels a specified distance away, which depends on the oscillation characteristics of the source. Results are tested against an analytical solution reported for a special case. The explicit finite difference method is shown to be effective for solving the advection-diffusion equation with constant coefficients in semi-infinite media with constant and oscillating boundary conditions.

Speeding up maximum population transfer in periodically driven multi-level quantum systems

A fast and robust approach to controlling the quantum state of a multi-level quantum system is investigated using a twofrequency time-varying potential. A comparison with other related approaches in the context of a two-level system is also presented, showing similar times and fidelities. As a concrete example, we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We show that the transition between the ground and first excited state is about 20 times faster than the one performed using a single frequency, both with fidelity of 99.97%. The transition time is about 3.5 times the minimum allowed by quantum mechanics. A test of the robustness of the approach is presented, concluding that, counter-intuitively, it is not only faster but also easier to tune up two frequencies than one. This robustness makes the approach suitable for real applications.

The impact of magnetohydrodynamics and heat transfer on the unsteady flow of Casson fluid in an oscillating cylinder via integral transform: A Caputo–Fabrizio fractional model

Casson fluid flow has numerous functional applications in food processing, metallurgy, drilling and bio-engineering operations. The significance of Casson fluid in cylindrical coordinates has recently attracted researchers because of the numerical and experimental analyses of the fluid. Due to the lack of fractional analytical approaches, this paper is trying to examine the magnetic effect and thermal effect on Casson fluid with oscillatory boundary conditions in cylindrical coordinates. The constitutive model of Casson fluid is solved by using the Caputo–Fabrizio time fractional derivative approach. The fluid moves in the vertical oscillating cylinder under the influence of a transverse applied magnetic field. Closed-form solutions are obtained via integral transforms (Laplace and Hankel transformations) for velocity and temperature distributions. Graphical results are shown for various physical parameters such as the Casson fluid parameter $$\beta $$ , magnetic parameter M, Grashoff number Gr, Prandtl number Pr and fractional parameter $$\alpha $$ . The corresponding expressions for Nusselt number are also evaluated for various embedded parameters in a tabular form.

Homogenization of the boundary value problem for the poisson equation with rapidly oscillating nonlinear boundary conditions: space dimension n ≥ 3, critical case

The homogenization of the Poisson equation in a bounded domain with rapidly oscillating boundary conditions specied on a part of the domain boundary is studied. A Neumann boundary condition alternates with an ε-periodically distributed nonlinear Robin condition involving the coefficient ε-β, where β ∈ R. The diameter of the boundary portions with a nonlinear Robin condition is of order O(εα), α > 1. A critical relation between the parameters α and β is considered