Set Of Nonlinear Equations Research Articles

Feasibility of integrated numerical and Adaptive Neuro-Fuzzy Inference System models in predicting the thermophysical properties of unsteady coupled micropolar–Casson hybrid nanofluids

This article aims to probe postulated phenomena using a paired micropolar and Casson hybrid fluid over a rotating disk. The intension to design a numerical technique (Runge–Kutta fourth-order along with shooting technique) integrated Adaptive Neuro-Fuzzy Inference System (ANFIS) envisioned with a thermal and exponentially space-dependent heat source, nonlinear thermal radiation and entropy production is developed in this phase of work. To ensure that, a nonlinear partial differential equation set of equations has been transformed into an ordinary differential equation by using the proper self-similarity variables. The model's research results, with a few notable outliers, are mostly consistent with those from prior research that was merged into the dataset used to train the ANFIS model. With the impact of active factors, the results are esthetically exhibited for numerous profiles. This displays that with the rise in magnetic field and radiation, the velocity and temperature profiles increase sharply, resulting in a contradiction phenomenon with the decreasing electric field inputs. Also, tilting of vortex viscosity, spin gradient viscosity and microinertia density on the various microrotation components displays inclination. Moreover, ANFIS training was exploited to analyze the approximate solutions for specific scenarios, and the developed ANFIS was evaluated against a testing dataset to emphasize its performance. Due to their longer render, the nanoparticles exploited here are deemed suitable for use in bone implants, iodinated agents for blood imaging and red blood cell stimulation. Thus, the results of this study may be applied to therapeutic anemia therapies.

Impact of the Stefan gusting on a bioconvective nanofluid with the various slips over a rotating disc and a substance-responsive species

This paper presents thorough computational and theoretical analyses of steady forced convective flow over a rotating disc submerged in a water-based nanofluid containing microorganisms. It delves into the examination of boundary layer flow characteristics of a viscous nanofluid, considering Stefan blowing effects and multiple slip conditions influenced by a magnetic field. Notably, the study accounts for novel aspects such as thermal radiation and both constructive and destructive chemical reactions. The movement of nanoparticles is elucidated based on thermophoresis and microscopic behaviors, while changes in volume fraction do not affect the thermo-physical properties of the nanofluid. To address the altered nonlinear set of differential equations, an effective numerical approach, the Keller-Box method, is implemented for critical and efficient solutions. These appropriate transformations are defined and applied. When compared to blowing suction, it shows a better enhancement in the rate of heat transfer, mass, and microorganisms. Some of the main observations are there is a decrease in wall skin friction in the directions of radial and tangential as magnetic field strength is increased. The evaluation of thermal boundary layer thickness and temperature is noted for the radiation parameter (Rd) improvement. The present analysis has applications in electromagnetic micro-pumps and nanomechanics. As to the applications in the science and engineering fields, technologies such as micro-electromechanical systems-based microfluidic devices and microfluidic-related technologies will be accepted.

Mixed Convection Flow of a Casson Fluid Past a Thin Needle

Mixed Convection Flow of a Casson Fluid Past a Thin Needle

Dynamics of energy transport on hydromagnetic Casson slippery nanoflow over curved surface

The study of fluid flow over curved surfaces is crucial in various engineering applications, such as designing aircraft wings, turbines, and submarines. Curved surfaces are being explored in various biomedical applications, such as designing stents for blood vessels and implants for bones and joints. Concerning the present applications of curved stretching sheets on fluid dynamics along with trihybrid nanofluids, this study is unique and fills the research gaps and offers solutions to several issues. This work looks at the flow through the boundary layer of an electrically conductive trihybrid nanofluid and the convection heat exchange of a Casson fluid across a curved stretched surface encircled within a circle of radius R. The study considers the effects of thermal radiation using the non-linearized Rosseland approximation, as well as a magnetic field, and hydromagnetic slip. The flow as well as the transfer of heat problem is mathematically described by curvilinear coordinates. Using the combination of the shooting technique and the Runge-Kutta method, similar solutions to the modeled partial differential equations are produced, and the set of non-linear ordinary differential equations with a boundary value solver is implemented through the MATLAB program. The study finds the influence of several limits on critical characteristics such as fluid velocity, coefficient of skin friction, pressure, temperature, and rate of heat exchange over a surface. The findings are shown in tables and graphs. Additionally, a comparative analysis between the current findings and those found in the literature is provided. Blood-containing nanoparticles (GO-SWCNTs-MWCNTs) on curved surfaces could improve drug delivery effectiveness, growth of synthetic tissues or organs with complex structures and effective cancer therapy treatment.

Pulsatile flow of blood and Cattaneo Christov heat flux model in diseased arteries with variable properties

ABSTRACT The current effort is executed to interpret the heat transmission of combined stenosis and aneurysm in an artery, taking into account variable properties such as viscous dissipation and thermal radiation. We reduced the two directional energy and momentum equations to unidirectional flow by normalizing them under the mild stenotic assumption. After that, a mathematical framework for the physical problem is developed. An intricate nonlinear set of partial differential equations results from this formulation. A suitable numerical method of finite difference is employed on consequent equations to solve them. Afterward, graphical results predict the region of flow and the influence of involved parameters is shown in pictorial form. Furthermore, these solutions are employed to test how certain parameters, like streamlines, flow rate, and wall shear stress, affect blood flow. Using streamlines, we will also observe the general behavior of blood flow patterns.

Numerical simulation of coupled Klein–Gordon–Schrödinger equations: RBF partition of unity

The coupled Klein–Gordon–Schrödinger equations have significant implications in quantum field theory, particle physics, cosmology, and nonlinear dynamics. In this study, we propose an efficient method for numerically simulating this system. The proposed approach involves employing the radial basis function partition of unity for spatial discretization. This method utilizes scaled Lagrange basis functions with polyharmonic spline kernels, taking advantage of the scalability property of the polyharmonic kernel to ensure stability in the approximation process. The resulting spatially discretized system yields a nonlinear time-dependent set of differential equations. To solve this system, we combine an implicit central finite difference scheme with a predictor–corrector procedure to overcome the nonlinearity. In the numerical results section, we assess the efficiency, accuracy, and versatility of the proposed method by conducting several simulations in large domains over extended periods. We present and compare these results with those obtained using alternative methods, demonstrating the effectiveness of the proposed approach in accurately solving the coupled Klein–Gordon–Schrödinger equations.

Exploration of thermal radiation and stagnation point in MHD micropolar nanofluid flow over a stretching sheet with Navier slip

The quest to strengthen heat conduction of thermal science base fluid for effective industrial outputs and engineering derives has recently increased. Thus, this study aims to determine how thermal radiation and slip effects affect the flow of a micropolar nanofluid near a stagnation point over an extending sheet. Using similarity transformations, the flow-controlling partial differential equations (PDEs) are turned into a set of non-linear ordinary differential equations (ODEs). The non-linear system of equations has been solved by the numerical technique Runge-Kutta-Fehlberg integration scheme implementing the shooting technique with suitable conditions to generate a numerical solution. The essential factors affecting the flow are depicted graphically and tabularly. Additionally, a comparison is conducted between the present result and previously published data on the Nusselt and Sherwood numbers; it claims that thermophoresis and Brownian motion vary under some restrictive conditions. An increase in the magnetic field parameter was found to boost the velocity of the micropolar nanofluid. In contrast, a rise in the micropolar parameter reduces the angular velocity.

Non-similar analysis of micropolar magnetized nanofluid flow over a stretched surface

The study of micropolar nanofluids unveils intriguing applications, propelled by their exceptional heat transfer capabilities in comparison to conventional fluids. This investigation focuses on analyzing the behavior of magnetized micropolar nanofluid flow over a stretched surface, taking into account crucial factors such as viscous dissipation and heat source. The chosen base fluid is blood, with Copper [Formula: see text] nanoparticles serving as the selected material. Incorporating the single-phase (Tiwari-Das) model with boundary layer assumptions for micropolar nanofluid flow, we introduce the volume fraction of nanoparticles to assess heat transport. The governing system undergoes transformation into a set of dimensionless non-linear coupled differential equations through appropriate transformations. This transformation involves the utilization of a combination of the local non-similarity technique and bvp4c (MATLAB tool) to derive the system of nondimensional partial differential equations (PDEs) for micropolar nanofluid. Our systematic exploration delves into the consequences of nondimensional parameters on velocity, microrotation, and temperature profiles within the boundary layer, including the Eckert number, micropolar parameter, magnetic field parameter, heat source, Prandtl number, and microorganism parameter. Graphical representations vividly demonstrate that the velocity and temperature of micropolar nanofluid increase with the rise in material parameter values, while the microrotation profile decreases. Increasing the magnetic field parameter leads to a reduction in the velocity profile. Moreover, the micropolar temperature profile shows an increase with the rising Eckert number. Crucially, the research emphasizes that factors like the heat source and Eckert number play a role in decreasing the local Nusselt number. In contrast, an increase in the local Nusselt number is observed for material parameters. Furthermore, the skin friction coefficient decreases as micropolar parameter values increase, whereas an increase in the skin friction coefficient is noted for the magnetic field. The primary focus of this research lies in the development of suitable non-similar transformations for the investigated problem, aiming to yield authentic and efficient results. These results hold substantial promise to make meaningful contributions to future research on nanofluid flows.

Flow Characteristics of Casson Nanofluid Over a Moving Wedge

Objectives: Analysis of Cassion nanofluid over a wedge is carried out for magnetohydrodynamics (MHD), wedge parameter, thermal radiation parameter, non-uniform heat source or sink and suction/injection parameter. Method: With the help of similarity transformations, the governing partial differential equations corresponding to the momentum and heat transfer are reduced to a set of non-linear ordinary differential equations. Numerical solutions of these equations are obtained. Findings: The influence of relevant parameters on non-dimensional velocity and temperature profiles are depicted graphically and in table form for two flow cases namely for nanofluid and for regular fluid. Novelty: It is experienced that with an escalation of magnetic field parameter, the flow is accelerated. Velocity profile shows growth with enhanced wedge parameter. Nusselt number and Skin friction parameters are discussed with the assistance of the table for base fluid and nanofluid. Keywords: Nanofluid, Suction, Injection, MHD, Casson fluid, Wedge

MHD boundary layer micropolar fluid flow over a stretching wedge surface: Thermophoresis and brownian motion effect

To investigate the consequence of thermophoresis and Brownian diffusion on convective boundary layer micropolar fluid flow over a stretching wedge-shaped surface. The effects of non-dimensional parameters namely coupling constant parameter (0.01 ≤ B1 ≤ 0.05), magnetic parameter (1.0 ≤ M ≤ 15.0), Grashof number (0.3 ≤ Gr ≤ 0.9), modified Grashof number (0.3 ≤ Gm ≤ 0.8), micropolar parameter (2.0 ≤ G2 ≤ 7.5), vortex viscosity constraint (0.02 ≤ G1 ≤ 0.2), Prandtl number (7.0 ≤ Pr ≤ 15.0), thermal radiation parameter (0.25 ≤ R ≤ 0.50), Brownian motion parameter (0.2 ≤ Nb ≤ 0.62), thermophoresis parameter (0.04 ≤ Nt ≤ 0.10), heat generation parameter (0.1 ≤ Q ≤ 0.5), Biot number (0.65 ≤ Bi ≤ 1.0), stretching parameter (0.2 ≤ A ≤ 0.5), Lewis number (3.0 ≤ Le ≤ 7.0), and chemical reaction parameter (0.2 ≤ K ≤ 0.7) on the steady MHD heat and mass transfer is investigated in the present study. The coupled non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations employing similarity transformation. Furthermore, by using the Runge-Kutta method followed by the shooting technique, the transformed equations are solved. The main goal of this study is to investigate the numerical analysis of nanofluid flow within the boundary layer region with the effects of the microrotation parameter and velocity ratio parameter. The novelty of this paper is to propose a numerical method for solving third-order ordinary differential equations that include both linear and nonlinear terms. To understand the physical significance of this work, numerical analyses and tabular displays of the skin friction coefficient, Nusselt number, and Sherwood number are shown. The new approach of the present study contributes significantly to the understanding of numerical solutions to non-linear differential equations in fluid mechanics and micropolar fluid flow. Micropolar fluids are becoming even more of a focus due to the desire for engineering applications in various fields of medical, mechanical engineering, and chemical processing.

Spin Drude weight for the integrable XXZ chain with arbitrary spin

Using generalized hydrodynamics (GHD), we exactly evaluate the finite-temperature spin Drude weight at zero magnetic field for the integrable XXZ chain with arbitrary spin and easy-plane anisotropy. First, we construct the fusion hierarchy of the quantum transfer matrices (T-functions) and derive functional relations (T- and Y-systems) satisfied by the T-functions and certain combinations of them (Y-functions). Through analytical arguments, the Y-system is reduced to a set of non-linear integral equations, equivalent to the thermodynamic Bethe ansatz (TBA) equations. Then, employing GHD, we calculate the spin Drude weight at arbitrary finite temperatures. As a result, a characteristic fractal-like structure of the Drude weight is observed at arbitrary spin, similar to the spin-1/2 case. In our approach, the solutions to the TBA equations (i.e. the Y-functions) can be explicitly written in terms of the T-functions, thus allowing for a systematic calculation of the high-temperature limit of the Drude weight.

Controlled random initialization of search vectors for application of gravitational search algorithm to selective harmonic elimination PWM

The prime objective of SHE PWM is to eliminate selected lower order harmonic by solving a set of non-linear transcendental equation while maintaining the fundamental component at a desired satisfactory value. In order to solve these non-linear equations different metaheuristic optimization techniques has been used in recent past. Due to faster convergence rate increased precision and higher probability to calculus based mathematical approximation techniques. In this manuscript an improved initialized Gravitational search algorithm has been proposed for a uni-polar 3-phase inverter. The algorithm is improved upon through a controlled random initialization of search agent, specifically for the purpose of solving the set of non-linear transcendental equation in SHEPWM for 3- switching angles. The simulation of the gravitational search algorithm and the proposed improved initialized GSA has been performed in MATLAB software and comparison of different performance parameter like Harmonic distortion, convergence rate etc. has been studied. The simulation results proves that a considerable improvement has been achieved by applying improved initialized GSA algorithm in terms of harmonic mitigation, convergence rate and accuracy in finding out the appropriate switching angles. Finally, the results obtained in simulation are verified through an appropriate experimental setup.

Blended ferron solitary wave emerging from electron–phonon–magnon interaction in magnetic clusters: Ferrons vs skyrmions

In this paper, the solitonic behaviour of a blended ferron in a ferromagnetic material is studied and the different spin configurations obtained are discussed. It is found that the electron–magnon–phonon coupling significantly affects the exchange between neighbouring spins and thus both the lattice and the spin are polarized. The dynamics of the model is well described by a set of nonlinear discrete self-trapped equations with stable resonant solutions. In terms of topology, the ferron configurations obtained mimic a skyrmion, while their induced polarization and magnetization are Bell-shape soliton-like. We observe that a significant presence of the Dzyaloshinsky–Moriya interaction topologically favours a vortex skyrmion configuration (Bloch’s skyrmion), while its absence restores a Neel’s skyrmion shape. Therefore, the blended ferron is manifested in the magnetic material by its localization and the formation of self-trapped states leading to skyrmion topology. This wonderful combination is a huge boost in skyrmion formation and thus the probable application to superconductivity are opened through skyrmion pairing.

Dynamics of vertical axis washing machines with uncertain unbalance

A washing machine is a household appliance that has an interesting and complex dynamical behavior, which can be well described by a set of nonlinear differential equations. When analyzing the dynamics of a washing machine, the steady state motion (periodic solution) is an important response to consider and can be evaluated as a solution of a periodic boundary-value problem. The unbalance generated by the unevenly distribution of clothes during centrifugation is highly random and, therefore, a stochastic model is necessary to take this characteristic into account. The novelty of this paper consists in the analysis of a washing machine dynamics considering the uncertainty in the unbalance. Therefore, a stochastic model is proposed for the dynamics of a washing machine. The steady state solutions are calculated using the shooting method combined with a sequential continuation to evaluate it across all the spin speeds of the machine. The probability distributions of the washing machine vibration at those different spin speeds are approximated using Monte Carlo simulations. The impact of the random unbalance in the vibration amplitude of the washing machine is also investigated and consists in a key input for the fatigue design of many components.

Numerical investigation on MHD non-Newtonian pulsating Fe 3 O 4-blood nanofluid flow through vertical channel with nonlinear thermal radiation, entropy generation, and Joule heating

The main aim of the present investigation is to examine the effect of nonlinear thermal radiation, slip, and Joule heating on MHD Pulsatile flow of third-grade ferro-nanofluid via vertical channel with entropy generation. The significance of this study is that it has plenty of physiological applications like cancer treatment, vitamin injections, dialysis, heart–lung machines during surgeries and industrial applications like filtration, pharmaceutical fluid production, and dispensing cosmetic/glue emulsions with no contamination. Furthermore, the ferro-nanoliquid model is the best model for numerous bio/industrial fluids. Therefore, this study explores the entropy analysis of pulsating third-grade ferro-nanoliquid flow between two parallel vertical walls under an applied magnetic field. Blood is taken as a base fluid (third grade), and iron oxide is used as nanoparticles. The governed nonlinear partial differential equations (PDEs) are nondimensionalized, and then the perturbation technique is employed to attain the set of nonlinear ordinary differential equations (ODEs). The bvp4c technique with MATLAB software is utilized to obtain the solutions for the set of ODEs. The deviations in several physical quantities on the flow variables are deployed via graphs. An increment in Eckert number and radiation parameter accelerates the temperature. Entropy generation rate and Bejan number are accelerated for greater values of radiation parameter. The values of the skin friction and Nusselt number against various physical parameters are presented in tables.

Adaptive Neural Tracking Control of a Class of Hyperbolic PDE With Uncertain Actuator Dynamics.

This article investigates the adaptive neural tracking control problem for a class of hyperbolic PDE with boundary actuator dynamics described by a set of nonlinear ordinary differential equations (ODEs). Particularly, the control input appears in the ODE subsystem with unknown nonlinearities requiring to be estimated and compensated, which makes the control task rather difficult. It is the first time to consider tracking control of such a class of systems, rendering our contributions essentially different from the existing literature that merely focus on the stabilization problem. By formulating a virtual exosystem to generate a reference trajectory, we propose a novel design of the adaptive geometric controller for the considered system where neural networks (NNs) are employed to approximately estimate nonlinearities, and finite and infinite-dimensional backstepping techniques are leveraged. Moreover, rigorously theoretical proofs based on the Lyapunov theory are provided to analyze the stability of the closed-loop system. Finally, we illustrate the results through two numerical simulations.

Polarization dependent gain in Raman fiber amplifiers with multiple pumps.

In this paper, the polarization dependent gain (PDG) in Raman fiber amplifiers (RFAs) with multiple pumps is studied thoroughly. A comprehensive model, which takes the random polarization mode dispersion, the nonlinear coupling between the pumps, and the degree of polarization (DOP) of the pumps into account, is proposed. The complex nonlinear and random coupling inside the optical fiber is described by a set of nonlinear stochastic differential equations (SDEs), which enable co-simulation of the polarized part and the depolarized part of the multiple pumps. It is revealed that the average PDG and the PDG standard deviation are linearly proportional to the DOP of the pumps, which agrees with the single mode case. More importantly, when the pump wavelength is far away from the signal amplification range (pump-signal wavelength difference larger than 100 nm), its DOP still affects the PDG of the signal. Such a phenomenon is caused by the fact that the pumps interact with each other and the pump DOP could transfer among the pumps, which could enhance the PDG of the RFA. The findings in the work will have important implications for the design of the optical transmission systems with the multi-pump RFAs.

Stagnation point flow for the dynamics of thermal enhancement in nanofluid by a convective extending surface with suction/injection and heat source

We intend to analyze the influences of heat dissipation and heat generation on steady nanofluid stagnated flow along an extending surface along with thermal boundary layers. Water-based Cu and Al2O3 nanoparticles are considered. Moreover, the mechanism of injection/suction has been analyzed for such flows. Fundamental governing equations for the flow of an isotropic in-compressible thermally radiative single-phase nanofluid are defined by the set of nonlinear Partial Differential Equations (PDEs) which are transmuted to Ordinary Differential Equation (ODEs) and dealt with numerically by using Runge–Kutta (RK) fourth-order adopting shooting technique that gives approximate simulations. The numerical findings are illustrated as graphical and tabular representations after a careful parametric examination of determined parameters is carried out. The current outcomes specify that the velocity profiles decrease under the influence of magnetic strength while heat distribution positively changes under the effect of magnetic strength, heat source, radiative term and Biot number quantity. The temperature profiles behave negatively with the thermal Grashof number and Prandtl number. Moreover, the comparative simulations of the ongoing study with existing the literature for ensuing the obtained simulations have been worked out.

Falkner-Skan Flow of Nanofluid with Convective Boundary Condition

This study focuses on the investigation of nanofluid flow with convective boundary conditions past a static wedge by considering copper as the chosen nanoparticles and water as the conventional base fluid. The governing partial differential equations (PDE) are transformed into a set of nonlinear ordinary differential equations (ODE) by using an appropriate similarity transformation. The transformed governing equations are then solved numerically by using the Keller-box method. The significant impact of parameters included wedge angle parameter, mixed convection parameter, volume fraction of nanoparticle and Biot number are presented. The graphical analysis on velocity and temperature profiles revealed that the increasing values of all considered parameters causes the increment of velocity of the flow. Meanwhile, significant changes on the temperature profiles are clearly depicted on the increment of nanoparticle volume fraction as well as the Biot number.

Flow over a stretchable cylinder with nonlinear heat sources/sinks: Magnetic dipoles application

This work contributes mainly an analysis of the impact of a generated magnetic dipole on the magneto heat transport inside a deformable cylinder. Magnetic dipole signifies, magnotherapy and spectroscopy which are medical applications, generate static magnetic fields. The investigation considers the influence of non-linear heat sources and sinks, which result in a noteworthy phenomenon. The flow field is governed by accurate and nondimensional factors, which are used to convert the initial set of highly nonlinear and coupled partial differential equations into a set of nonlinear ordinary differential equations. These nonlinear ordinary differential equations are then solved mathematically using the bvp4c function in MATLAB, taking into account the boundary conditions. Ultimately, this section provides an overview of the ramifications stemming from various physical constraints on the movement of fluids, including nonlinear source/sink effects and other more factors. Ultimately, the discovered results that impose limitations are juxtaposed with those documented in the scientific literature, revealing a significant connection.