Set Of Differential Equations Research Articles

Efficient passive GDQLL scrutinization of an advanced steady EMHD mixed convective nanofluid flow problem via Wakif–Buongiorno approach and generalized transport laws

Owing to the practical importance of nanofluids and their adjustable thermal capabilities, this study intends to develop a robust generalized differential quadrature local linearization (GDQLL) algorithm for examining realistically the heat and mass aspects of electrically conducting nanofluids during their non-Darcian laminar motion nearby a convectively heating vertical surface of an active electromagnetic actuator (i.e., Riga plate). By invoking Wakif–Buongiorno model and Oberbeck–Boussinesq approximations along with other generalized transport laws (i.e., Cattaneo–Christov and non-Fick’s laws) and Grinberg’s concept, a set of gigantic partial differential equations is stated appropriately in the sense of the boundary layer approximations for describing exhaustively the present EMHD mixed convective nonhomogeneous flow under the passive control strategy of nanoparticles within the nanofluidic medium. Operationally, the dimensionless differential forms of the governing boundary equations are derived properly by introducing reasonable mathematical adjustments into the preliminary formulation. In this case, the differential complexity of the leading differential structure is reduced to a nonlinear coupled system of ordinary differential equations, whose discrete numerical solutions are computed perfectly via a well-structured GDQLL algorithm. As foremost outcomes, it is demonstrated that the nanofluid motion and its surface thermal enhancement rate can be reinforced significantly through the thermal strengthening in the convective heating and mixed convective process as well as via the electromagnetic improvement in the driven aspect of Lorentz’s forces.

Analysis of unsteady MHD fluid flow across two parallel discs with uniform fluctuation subject to modified Hall and activation energy

This study intends to examine the consequences of the externally applied magnetic field and modified Hall effect on nanofluid flow across two symmetrically spinning and extending discs, where continuously the upper disc moves upward and downward. The lower disc is vertically fixed. The discs rotate and move vertically, generating a 3D flow. The mass density, heat transfer and flow motion have been evaluated and modeled in the form of the system of partial differential equations (PDEs) with an additional influence of activation energy, heat source and chemical reaction. The system of PDEs is modified to an ordinary set of differential equations by employing the resemblance substitution method. The obtained system of ODEs is further solved through the numerical approach (bvp4c). The results are compared to the bvp4c package and published work for validity purposes. In the case of downward displacement of the upper disc, magnetic and Hall characteristics have a significant impact on the velocity curve. The energy curve elevates with the upward movement of the disc, while it reduces with the downward fluctuation. Furthermore, the mass transmission rate enhances with the influence of hall current, while diminishing with the impact of chemical reaction rate.

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.

Influence of Gyrotactic Microorganisms on Bioconvection in Electromagnetohydrodynamic Hybrid Nanofluid through a Permeable Sheet

Many biotechnology sectors that depend on fluids and their physical characteristics, including the phenomenon of bioconvection, have generated a great deal of discussion. The term “bioconvection” describes the organized movement of microorganisms, such as bacteria or algae. Microorganisms that participate in bioconvection display directed movement, frequently in the form of upward or downward streaming, which can lead to the production of distinctive patterns. The interaction between the microbes’ swimming behavior and the physical forces acting on them, such as buoyancy and fluid flow, is what drives these patterns. This work considers the laminar-mixed convection incompressible flow at the stagnation point with viscous and gyrotactic microorganisms in an unsteady electrically conducting hybrid nanofluid (Fe3O4-Cu/water). In addition, hybrid nanofluid flow over a horizontal porous stretched sheet, as well as external and induced magnetic field effects, can be used in biological domains, including drug delivery and microcirculatory system flow dynamics. The governing system has been reduced to a set of ordinary differential equations (ODEs) through the use of the group technique. The current research was inspired by an examination of the impacts of multiple parameters, including Prandtl number, Pr, magnetic diffusivity, η0, shape factor, n, microorganism diffusion coefficient, Dn, Brownian motion coefficient, DB, thermophoresis diffusion coefficient, DT, bioconvection Peclet number, Pe, temperature difference, δt, and concentration difference, δc. The results show that as Pr rises, temperature, heat flux, and nanoparticles all decrease. In contrast, when the η0 value increases, the magnetic field and velocity decrease. Heat flow, bacterial density, and temperature decrease as the DB value rises, yet the number of nanoparticles increases. As the DT value increases, the temperature, heat flow, and concentration of nanoparticles all rise while the density of bacteria decreases. Even though temperature, heat flux, nanoparticles, and bacterial density all decrease as δc values climb, bacterial density rises as Dn values do although bacterial density falls with increasing, δt and Pe values; on the other hand, when n values increase, temperature and heat flow increase but the density of bacteria and nanoparticle decrease. The physical importance and behavior of the present parameters were illustrated graphically.

Modeling the hydromagnetic transient three-dimensional stagnation point flow of a couple stress Casson fluid over a bi-directional stretching sheet

A numerical study is performed to examine the magnetohydrodynamic effects on the transient three-dimensional stagnation point flow of a Casson fluid along a bi-directional stretching sheet. The physical model of the flow includes a sheet which is stretched in both the tangential directions and is thus called “bi-directional stretching”. The heat transfer mechanism includes the influences of space- and time-dependent non-uniform heat generation/absorption, as well as dissipation due to viscosity. The mathematical modeling of the problem involves the constitution of a set of coupled nonlinear boundary layer equations, together with suitable boundary conditions. The mathematical model thus developed is then subjected to suitable similarity transformations to arrive at a set of ordinary differential equations, which were then treated with the successive linearization method (SLM) to obtain approximate solutions for the velocity and temperature fields. A parametric study is carried out, and the results are discussed and presented graphically to analyze the behavior of the primary and secondary velocity distributions, as well as fluid temperature, along with significant physical quantities such as skin friction and Nusselt number for various values of the nondimensional parameters. Multiple quadratic regression analysis is also carried out to investigate the significance of parameters and to estimate the skin-friction and heat transfer coefficients.

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.

Spectral-based optimal output-feedback boundary control of a cracking catalytic reactor PDE model

This research paper focuses on the design of a boundary optimal controller with output feedback for a tubular catalytic cracking reactor. The process is represented by a set of non-linear parabolic partial differential equations (PDEs). The approach involves utilising the linearised infinite-dimensional version of the model, taking advantage of the system generator being a Riesz spectral operator. A stabilising compensator is designed by leveraging the eigenvalues and eigenvectors of the system generator. This paper also includes numerical simulations to demonstrate the performance of the developed algorithm.

Mathematical modeling of fluid dynamics in invitro gut fermentation systems: A new tool to improve the interpretation of microbial metabolism.

In vitro systems are widely employed to assess the impact of dietary compounds on the gut microbiota and their conversion into beneficial bacterial metabolites. However, the complex fluid dynamics and multi-segmented nature of these systems can complicate the comprehensive analysis of dietary compound fate, potentially confounding physical dilution or washout with microbial catabolism. In this study, we developed fluid dynamics models based on sets of ordinary differential equations to simulate the behavior of an inert compound within two commonly used invitro systems: the continuous two-stage PolyFermS system and the semi-continuous multi-segmented SHIME® system as well as into various declinations of those systems. The models were validated by investigating the fate of blue dextran, demonstrating excellent agreement between experimental and modeling data (with r2 values ranging from 0.996 to 0.86 for different approaches). As a proof of concept for the utility of fluid dynamics models in invitro system, we applied generated models to interpret metabolomic data of procyanidin A2 (ProA2) generated from the addition of proanthocyanidin (PAC)-rich cranberry extract to both the PolyFermS and SHIME® systems. The results suggested ProA2 degradation by the gut microbiota when compared to the modeling of an inert compound. Models of fluid dynamics developed in this study provide a foundation for comprehensive analysis of gut metabolic data in commonly utilized invitro PolyFermS and SHIME® bioreactor systems and can enable a more accurate understanding of the contribution of bacterial metabolism to the variability in the concentration of target metabolites.

Numerical Investigation of Nanofluid as a Coolant in a Prismatic Battery for Thermal Management Systems

Abstract This study delves into the realm of numerical investigation of the heat transfer performance of nanofluids as coolants for prismatic batteries. Nanofluids are being employed in battery cooling systems to enhance overall thermal management and ensure the safe operation of batteries, particularly in situations involving high heat generation. In this study, different types of nanofluids were used along with a base fluid of ethylene glycol–water (EG–water 50%). The energy equations consider the effects of viscous dissipation and heat generation. The model generates a set of nonlinear partial differential equations, which can be transformed into ordinary differential equations (ODEs) using appropriate similarity variables. These ODEs are then solved numerically by employing the Runge–Kutta–Fehlberg method along with the shooting method to obtain solutions. The simulations in both 2D and 3D showcase the results for various parameters pertaining to thermal and velocity fields, heat transfer rate, and drag force. The findings reveal that heat generation leads to a staggering increase in temperature of 78.22%. However, using aluminum nanoparticles (NPs) as opposed to copper nanoparticles quickly reduced the battery’s maximum temperature by 9.31%. The exceptional heat generation strengths of CuO–EG and Al2O3–EG nanofluids also resulted in a significant increase in their heat transfer rates of around 40.42% and 42.13%, respectively. Additionally, the aluminum NPs exhibited a more rapid heat transfer rate of 4.06% when compared to the copper nanoparticles. This research contributes to the development of improved cooling strategies for prismatic battery applications, ultimately paving the way for enhanced battery performance, an extended lifespan, and improved safety in a wide range of industries and electric vehicles.

Exploring entanglement dynamics in an optomechanical cavity with a type-[formula omitted] qutrit and quantized two-mode field

In this work, the main objective is to measure the degree of interaction of a type-V qutrit with a two-mode quantized field in an optomechanical cavity. To achieve this objective, we first deduce the Hamiltonian in the interaction picture to identify the oscillatory terms. Using the Coarse-Grained Method (CGM), we obtain the effective Hamiltonian analytically. By selecting initial conditions for the atom, the two-mode field, and the moving mirror, we can determine the state vector of the entire system through a first-order approximation of the effective Hamiltonian. With this information, we proceed to solve the Schrödinger equation, generating a coupled set of differential equations that is solved numerically based on the initial conditions. In this context, the atomic von Neumann entropy allows us to obtain the temporal evolution of the degree of entanglement of the qutrit in the cavity and the atomic population inversion. The results indicate that entanglement in this tripartite system, composed of the qutrit and the mirror-field subsystems, as well as the population inversion, can be manipulated by the initial state conditions of the system, the qutrit-field and mirror-field coupling coefficients, the pump field, and the dissipation rates of the two-mode field and the movable mirror, respectively.

A 1D model for the dynamic instability of magnetized beams in leakage flow energy harvesters

This paper presents a one-dimensional fluid–structure interaction model for investigating the dynamic stability of elastic mounted beams under the influence of magnetic forces in a leakage flow energy harvesting environment. The interaction between the beam and external magnetic fields is represented by a nonlinear long range force distribution that is non linearly dependent on the beam displacement. The formulation results in a two way coupled fluid–structure interaction system that is one way coupled with the electromagnetic system. A perturbation technique is utilized to linearize the second order equilibrium equations of the coupled system, which are then transformed into a set of first-order ordinary differential equations in the state space. The effect of the linearized magnetic force coefficient on the eigenvalues and dynamic stability of the system is analyzed through a parametric study. The results indicate the onset of oscillatory dynamics in the coupled magneto-fluid-structural system is a non monotonic function of the magnetic force.

Equations describing semi-confluent cell growth (I) Analytical approximations

A set of differential equations with analytical solutions are presented that can quantitatively account for variable degrees of contact inhibition on cell growth in two- and three-dimensional cultures. The developed equations can be used for comparative purposes when assessing contribution of higher-order effects, such as culture geometry and nutrient depletion, on mean cell growth rate. These equations also offer experimentalists the opportunity to characterize cell culture experiments using a single reductive parameter.

Time-dependent simplified [formula omitted] approximation for neutron transport equation

Time-dependent transport is still too computationally expensive for various practical purposes. On the other hand, the diffusion approximation is unable to provide accurate results for many real problems. To establish a middle ground between the accuracy of the transport and the simplicity of the diffusion approximations, the simplified spherical harmonics (SPN) method was introduced. The present paper aims to improve the accuracy of the time-dependent SP3 method by employing the simplified double-P1 (SDP1) approximation, which is based on the one-dimensional double-spherical harmonics DP1 equations. Using the finite element method to treat the spatial dependence of the SDP1 equations leads to a set of first-order ordinary differential equations on the time variable. These equations are then converted into a set of linear algebraic equations by discretizing the time variable with the implicit backward finite difference scheme. Our numerical results indicate that the SDP1 approximation could compute more precise values than the widely used SP3 method in transient problems.

IMPORTANCE OF THERMAL CONDUCTIVITY MODELS IN ANALYZING HEAT TRANSFER OF RADIATIVE HYBRID NANOFLUID ACROSS A STRETCHING SHEET USING DARCY-FORCHHEIMER FLOW

Hybrid nanofluids' enhanced thermal efficiency has important applications in many fields of industry and engineering. The goal of this study is to find out how different thermal conductivity models affect important factors in the Darcy-Forchheimer flow and heat transfer of a hybrid nanofluid made of Al<sub>2</sub>O<sub>3</sub> - Cu and water across a moving surface that can let some fluid pass through it. Magnetohydrodynamics (MHD), thermal radiation, joule heating, and viscous dissipation are all included in the study. Partial differential equations (PDEs) are made more manageable by reducing them to a set of ordinary differential equations (ODEs) via a similarity transformation. After that, Mathematica’s shooting technique and the Runge-Kutta algorithm are used to numerically solve these ODEs. The study analyzes the effects of key factors on the major physical quantities of interest and presents the findings graphically and tabularly. The research also shows that differing thermal conductivity models lead to significantly varied average Nusselt values. The rate of heat transmission improves with the addition of (φ<sub>2</sub> and S. The Xue model in the hybrid nanofluid shows a 0.7% increase in heat transfer rate compared to the nanofluid, while the Maxwell model shows a 0.64% increase and the Yamada-Ota model shows a 1.01% increase. Importantly, for all the considered models of thermal conductivity, the research shows that the average Nusselt number increases linearly with the nanoparticle volume percentage. Finally, the data shows that the Yamada-Ota model consistently produces far higher average Nusselt values than the other models.

A Novel Approximation Approach for the Analytical Solution of the Flow of Micropolar Fluid Through a Permeable Channel

An attempt is made in this study to investigate the problem of micropolar fluid flow in a porous medium theoretically. Employing the Berman’s similarity solution, the model equations governing the flow is transformed into a set of nonlinear ordinary differential equation and solved using Temimi-Ansari method. Expressions for the velocity and micro-rotation profiles are obtained under the impressions of diverse parameters affecting the flow problem. Using symbolic computation software Mathematica, the nondimensional equations are solved numerically using the Keller Box scheme. Comparison between the analytical solution obtained by TAM and the numerical result are compared with results in literature to observe rapid convergence. Findings from the study showed in the presence of

Mathematical Analysis of Fractional Diabetes Model via an Efficient Computational Technique

Diabetes is referred to a chronic metabolic disease signalized by elevated levels of blood glucose (also known as blood sugar level), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. A mathematical assessment of the diabetes model using the Caputo fractional order derivative operator is given in this research paper. The concept of a Caputo fractional order derivative is a novel class of non-integer order derivative that has many applications in real-life scenarios. The proposed model is represented by a set of fractional ordinary differential equations. The authors employed the Sumudu Transform Homotopy Perturbation Method (STHPM) for finding the series solutions of the model being studied. By giving various numerical values to the respective model parameters, graphical analysis is also performed. It is observed in the numerical discussion that a decrease in both fractional order and leads to decrease in the number of diabetic people.

Modeling, analyzing and simulating the dynamics of Tuberculosis-Covid-19 co-infection

Covid-19 and tuberculosis (TB) are two significant infectious illnesses that may pose significant threats to the public health and their co-infection aggravates the issue. Through the use of a set of nonlinear ordinary differential equations and contaminated surfaces from SARS-CoV-2 in the environment, we developed and investigated a mathematical model in this study for the dynamics of the co-infection of Covid-19 and TB transmission. The free equilibrium point of the disease was determined and its stability was investigated. The next generation matrix approach is used to determine the model’s basic reproduction number. The disease-free equilibrium point is not globally asymptotically stable, but it is locally asymptotically stable if R0 < L We found key model parameters for disease dynamics spread using normalized forward sensitivity analysis. From the numerical simulation results, we conclude that government stakeholders should work in reducing the transmission mechanisms of both diseases. In addition, they should look on mechanisms for removing SARS-CoV-2 contaminated surfaces from the community.

Event-Triggered Distribution System State Estimation: Sparse Kalman Filtering With Reinforced Coupling

A novel distribution system state estimation (DSSE) method is proposed for power distribution networks with low-observablity, where the measurements come from only a few distribution-level phasor measurement units (D-PMUs). The proposed DSSE method is event-triggered, which means the state variables are updated based on the information that is extracted from the events in the power distribution system. In this regard, the estimations of the state variables during the previous events are used as priori information to predict the state variables at the current event. Accordingly, a novel data-driven method based on elastic net regression analysis is proposed to learn the event-triggered state transition matrix. The DSSE problem is formulated as a generalized group Lasso problem, which is augmented based on the knowledge on the sparsity patterns of the state variables that are extracted from the analysis of the events. Here, in the absence of direct power measurements, we enhance our ability in sparse recovery by developing a new reinforced physics-based coupling method among the state variables, in which we add a novel set of linear differential power flow equations to the DSSE problem formulation in forms of virtual measurements. Finally, two different approaches are proposed to solve the formulated sparse event-triggered DSSE problem. The first approach is exact but computationally expensive, as it requires conducting a batch alternating direction method of multipliers (ADMM) analysis. The second approach is approximate, but it is much faster as it works based on a novel modified Kalman filter/smoother in the presence of ℓ1-norm.

Hydrodynamic Model for Particle Beam-Driven Wakefield in Carbon Nanotubes

The charged particles moving through a carbon nanotube (CNT) may be used to excite electromagnetic modes in the electron gas produced in the cylindrical graphene shell that makes up a nanotube wall. This effect has recently been proposed as a potential novel method of short-wavelength-high-gradient particle acceleration. In this contribution, the existing theory based on a linearized hydrodynamic model for a localized point-charge propagating in a single wall nanotube (SWNT) is reviewed. In this model, the electron gas is treated as a plasma with additional contributions to the fluid momentum equation from specific solid-state properties of the gas. The governing set of differential equations is formed by the continuity and momentum equations for the involved species. These equations are then coupled by Maxwell’s equations. The differential equation system is solved applying a modified Fourier-Bessel transform. An analysis has been realized to determine the plasma modes able to excite a longitudinal electrical wakefield component in the SWNT to accelerate test charges. Numerical results are obtained showing the influence of the damping factor, the velocity of the driver, the nanotube radius, and the particle position on the excited wakefields. A discussion is presented on the suitability and possible limitations of using this method for modelling CNT-based particle acceleration.

Water-based Fe2 O3 Ferrofluid Flow over a Rotatable Plate

In the current work, the influence of rotational viscosity as a result of an external magnetic field on water-based Fe2O3 ferrofluid flow over a rotating plate is investigated. The governing equations of the physical model are transformed into a set of ordinary differential equations. The numerical solution of the differential equations is obtained by using the finite element method. The findings of the radial, tangential, and axial velocity distributions are descriptively presented for the different range of rotational viscosity The outcomes of this research demonstrate that the magnetic field has an important role in controlling the velocity profiles in the flow. A comparative study of velocity distributions is presented for COFe2O4, Fe2O3, NiO, and CO nanoparticles.