Akbari-Ganji's Method Research Articles

Numerical and analytical investigation of Jeffrey nanofluid convective flow in magnetic field by FEM and AGM

In the present research, a numerical and analytical study on magnetohydrodynamic (MHD) convective flow of Jeffrey nanofluid has been presented. Investigation of mass and heat transfer phenomena has been done using mathematical modeling and considering thermal radiation. Solving and developing non-linear differential equations is done using finite element method (FEM) and Akbari-Ganji method (AGM). The novelty of this research lies in its application of these methods to investigate the effects of varying physical parameters on Jeffrey nanofluid flow, thereby filling a significant gap in the field of magnetohydrodynamics (MHD). Non-linear equations for energy, momentum and concentration are converted into dimensionless nonlinear equations by using appropriate variables. The main goal of this study is to determine the effect of various physical parameters on velocity, temperature and fluid concentration with the finite element model. This particular model was chosen because of the important role of magnetohydrodynamics and its wide applications in industry, engineering and medicine. The obtained results are presented graphically. It can be seen that with the increase of the mixed convection parameter, the velocity field increases, but the temperature and concentration decrease. Increasing the Hartmann number increases the speed and decreases the temperature in a certain range. When the Prandtl number increases, the temperature decreases. An increase in the Schmidt number results in a decrease in concentration. The results of the present study are in good agreement with the previous results, which shows the high accuracy and efficiency of the techniques used in this study.

Innovative binary nanofluid approach with copper (Cu - EO) and Magnetite ([formula omitted] - EO) for enhanced thermal performance

In this study, we present an innovative and detailed analysis of the motion of a binary nanofluid, specifically copper (Cu - EO) and Magnetite (Fe3O4 - EO), in a porous medium under solar radiation. Our research is driven by the potential to significantly enhance the thermal performance of a Parabolic Trough Solar Collector (PTSC) using a binary nanofluid. The boundary conditions, partial differential restrictions, and the governing PDEs are transformed into the ODEs system with appropriate similarity transformations. The finite element method (FEM) and semi-analytical technique memad Akbari-Ganji's Method (AGM) are used to solve the approximate solutions of ODEs. The findings of evaluating Copper (Cu - EO) and Magnetite (Fe3O4 - EO) were the two different nanofluids based on engine oil that were presented. Furthermore, the model's overall entropy variations are enhanced using Reynolds. Moreover, our study contributes to understanding fluidity and viscosity alterations in such systems. We use the Brinkman number to observe these alterations. We reveal that the thermal efficiency of (Cu - EO) is lower than (Fe3O4 - EO) by a range of 0.005–0.6. This indicates a substantial enhancement in the thermal performance of the PTSC.

Heat and mass transfer conduct in an unsteady two- dimensional stream between parallel sheets

In the present research, an effort has been made to analytically solve heat and mass linear/ nonlinear as well as steady/ unsteady equations in a viscous nanofluid squeezed between parallel sheets. Using Python and the SymPy library, the nanofluid with viscous properties between parallel sheets has been analyzed to symbolically solve flow, heat, and mass transfer effects equations through the Homotopy Perturbation Method and Akbari-Ganji Method approaches. The two nanofluids selected to conduct this study are Copper as well as Al2O3, whose sizes are 29 nm and 47 nm respectively. The provided details encompass the outcomes of active variables on flow and the transfer of heat coupled with mass. The Homotopy Perturbation and Akbari-Ganji methods have resulted in top-of-the-line consequences compared to analytical and numerical approaches. This research study highlights a faster and more accurate computation to conduct the analytic section of the study. The outcome shows that the increase of the Prandtl number and the Eckert number will increase Nusselt. However, skin friction increases with the increase in the Schmidt number. Furthermore, a rise in Schmidt number and parameters related to chemical reactions leads to an elevated Sherwood number. The outcomes of the study presented here provide a more innovative and precise insight, and the comparison with the available literature also proves there is a well-agreed numerical calculation. Microchips in engineering and medical-related industries would enjoy the outcomes obtained from this study. This study proves that the maximum and minimum amounts of heat transfer in respect occur at η=0 and η=1. Moreover, the maximum and minimum amounts of error are equal to 0.0001 and 0.00001, respectively. The maximum and minimum amounts of concentration occur at η=1 and η=0 in order. Finally, the maximum and minimum amounts of error are equal to 0.000016 and 0.000002, respectively.

Mathematical analysis of non-linear boundary-value problems in reaction-diffusion model of chitosan-alginate microsphere using homotopy perturbation and Akbari-Ganji methods

This article describes the non-linear reaction-diffusion model, which depicts the behaviour of hydrogen peroxide production and glucose oxidation in the chitosan-alginate microsphere. Analytical solutions of glucose, oxygen, gluconic acid and hydrogen peroxide concentrations in planar coordinates under steady-state circumstances are obtained for all reaction-diffusion parameters. The non-linear boundary value problem's approximate analytical expressions are obtained using asymptotic techniques based on the homotopy perturbation and Akbari-Ganji method. The exact and commonly used MATLAB program provided a numerical simulation. It is demonstrated that the resulting analytical expressions strongly agree with the numerical outcomes reported in the literature. Furthermore, determining hydrogen peroxide flux and pH profiles within the microspheres are also discussed. The theoretical findings make it possible to forecast and enhance the efficiency of enzyme kinetics.

Investigating the magnetohydrodynamics non-Newtonian fluid movement on a tensile plate affected by variable thickness with dufour and soret effects: Akbari Ganji and finite element methods

Significant progress in the investigation of non-Newtonian Williamson and Casson boundary layer flow has led us to explore the extension of non-Newtonian Williamson and Casson hydromagnetic boundary layer flow in an electrically conductive fluid subjected to a strong magnetic field and a uniform thermal field. This study is divided into two interconnected parts. The first part converts the nonlinear system governing the Partial Differential Equations into a simpler, nonlinear, ordinary differential equation. It is then analyzed using the Akbari Ganji method (AGM). The output data from the first part, solved using AGM, is compared and evaluated with the output data from the second part, solved with the assistance of finite element (FEM) methods. This research validates previous works with current methodologies. Subsequently, changes in temperature and concentration parameters, influenced by variations in magnetic parameters, are obtained and analyzed through three-dimensional charts. Upon reviewing the results, it is observed that the distribution of concentration and temperature is dependent on the distribution of the magnetic parameter, with an increase in concentration and temperature being influenced by the rise in the magnetic parameter. Other parameters are also examined, each of which is elaborated upon below. The effects of Bi1, Sr, and Sc parameters on temperature are investigated, and design points for achieving optimal and effective design are presented in the graph. Some applications of magnetohydrodynamics and non-Newtonian fluids include improving fluid pumping technologies. Using magnetohydrodynamics in non-Newtonian fluid pumping systems can help improve efficiency and reduce energy costs. Additionally, enhancing the efficiency of heat transfer systems using magnetohydrodynamics can help improve efficiency and reduce energy losses in these systems.

Mathematical Analysis of Nonlinear Differential Equations in Polymer Coated Microelectrodes

A theoretical analysis is conducted on the electrochemical behaviour of micro disk electrodes coated with thin coatings of electroactive polymers. The main focus of efforts to characterize the planar diffusion chemical reaction within polymer-modified ultra-microelectrodes is the creation of a theoretical model that explicitly takes into account the potential for the polymer film to cover the inlaid micro disc support surface. Approximate formulae for the steady-state amperometric response and formulation of the boundary value problem are given. The impact of substrate concentration, mediator concentration and current responsiveness in the solution besides the polymer film is also investigated. Akbari-Ganji method (AGM) and differential transformation method (DTM), two adequate and widely available analytical methods, were utilized to determine the steady-state non-linear diffusion equation. The approximate analytical solution for the substrate concentration and mediator concentration and the current for the small experimental kinetic values and diffusion coefficients are presented. We additionally determine the problem’s numerical solution using the MATLAB tool. A satisfactory agreement can be seen when the numerical outcomes verify with the analytical findings.

Studying the effects of electro-osmotic and several parameters on blood flow in stenotic arteries using CAGHPM

In this investigation, a new approach is proposed to study blood flow through a stenotic artery under the impact of electro-osmosis and several other main parameters. The new approach depends on the Chebyshev series, the Akbari-Ganji method, and the new homotopy perturbation method named the Chebyshev Akbari-Ganji homotopy perturbation method (CAGHPM). The validity of the proposed method was ensured by the good agreement of its results with the results obtained by other methods mentioned in previous studies. The influences of the electro-osmotic parameter and the Helmholtz-Smoluchowski velocity, as well as the inclination angle, magnetic field, porosity, and chemical reaction, are discussed in terms of the velocity, temperature, wall shear stress, and concentration of blood flow. The results obtained by using the CAGHPM are more accurate than those obtained by other methods used to solve the current problem. Furthermore, error tables, figures, and convergence analysis theoretically and computationally show the efficiency and effectiveness of the proposed new method.

Employing the Akbari Ganji Method (AGM) to conduct a semi-analytical analysis of transient Eyring-Powell compressible flow in a tensile Surface under the influence of a magnetic field

This study explores the transfer of mass and heat within unstable two-dimensional flows of non-Newtonian material under conditions involving radiation generation, absorption, and thermal radiation. Additionally, it investigates the impact of magnetic hydromagnetic joule (MHD) heating on these processes. The researchers converted the partial differential equations into ordinary ones through appropriate transformations. Subsequently, a new idea was considered, involving coupling fractional differential equations using the AGM method, with an order of 0.5 < a <0.8 and the initial condition x (0) = x0. A new technique is introduced to find the exact solution of fractional differential equations by solving the correct order differential equations. The primary aim of this paper is to explore the impact of parameter variations on velocity, temperature, local skin friction coefficient, and local Nusselt and Sherwood numbers. This article investigates the effect of multi-parameter changes on local skin friction coefficient and Schmidt number. In most fluid heat transfer problems, especially in non-Newtonian fluids, fractional differential equations are widely used in liquids. The obtained results indicate that the Lorentz force, influenced by the magnetic field parameter (Ha), diminishes the velocity distribution. Additionally, it is observed that the temperature profile decreases as the radiation parameter (R) increases.

New insights into MHD squeezing flows of reacting-radiating Maxwell nanofluids via Wakif's–Buongiorno point of view

AbstractThis work presents a computational investigation of a squeezing nanofluid flow under the influence of thermal radiation, magnetohydrodynamics (MHD), and chemical process in a constrained parallel-wall geometry. In this study, the non-Newtonian behavior of a rate-type (Maxwell) nanofluid is captured by rheological expressions that serve as the foundation for the flow formulation. This kind of thinking makes it possible to simulate the intricate nanofluid behavior that incorporates the elastic and viscous responses, which are useful in a variety of situations related to nanofluid dynamics, rheology, and materials science. Additionally, the transport equations are modeled properly using Wakif's–Buongiorno nanofluid model. The equations reflecting the dynamics of the nanofluid and heat-mass transport are developed based on admissible physical assumptions, such as the negligible viscous dissipation as well as the lower magnetic Reynolds number. After that, several similarity variables are introduced in these equations to get the dimensionless formulation form. Akbari–Ganji's method is used to carry out extensive computational simulations. Our results show that the increased squeezing parameters lead to larger horizontal and vertical velocities. On the other hand, the temperature showed a reverse relationship with the increasing squeezing parameters and exhibiting a cooling impact.

Investigate the influence of various parameters on MHD flow characteristics in a porous medium

The flow phenomena become more significant and varied when an extra heat source, a chemical reaction, and thermal and solutal buoyancy forces exist. Transport property optimization results from the current demand in several sectors dependent on the solutal reactant and the heat source given. Partial differential equations are transformed into ordinary equations using appropriate similarity transformations. Python was used as an efficient tool to solve equations in this research. According to the available facilities and libraries, Python can efficiently solve various physics and engineering problems. The homotopy perturbation method (HPM) and Akbari-Ganji Method (AGM) have been used to solve differential equations. The results calculated in Python indicate the high accuracy of calculations in Python. The effect of different parameters on the profile of velocity, temperature, and concentration has been investigated graphically. Also, the friction coefficient (Cf), Nusselt number (Nu), and Sherwood number (Sh) have also been investigated in this study. The results show that the velocity profile decreases with increased magnetic field intensity. Also, the porosity parameter has an inverse effect on the velocity and temperature profile, so the growth of the porosity parameter reduces the fluid velocity while improving the temperature profile.

Non-Fourier Heat Flux Model for the Magnetohydrodynamic Casson Nanofluid Flow Past a Porous Stretching Sheet using the Akbari-Gangi Method

The Casson fluid flow with porous material in magnetohydrodynamics is examined in this work. Additional semi-analytical results are investigated using the Silver-Water nanofluid. The Akbari-Ganji Method (AGM) is used to solve the semi-analytical Cattaneo-Christov heat flux model after taking thermal radiation into account. With the use of appropriate parameters, such as the relaxation time parameter, Prandtl number, radiation parameter, magnetic parameter, and so on, the normalized shear stress at the wall, temperature profile, and rate of heat flux may be examined. This issue has numerous industrial applications and technical procedures, such as the extrusion of rubber sheets and the manufacture of glass fiber. The main physical application is the discovery that a rise in the thermal relaxation parameter and Prandtl number maintains a constant fluid temperature.

MHD Casson non-Newtonian fluid flow in a channel with expanding/contracting porous walls in the presence of thermal radiation

In this research, we explore the impact of changing viscosity in the context of the asymmetric laminar flow of Casson fluid with thermal radiation. The flow occurs within a channel that can either expand or contract, featuring porous walls. The flow equations are converted into ordinary differential equations (ODEs) through appropriate transformations to simplify the analysis. The velocity field and temperature profile expressions are obtained using Akbari-Ganji's method (AGM) and finite-element method (FEM). The graphs show the impact of different parameters on the flow characteristics, especially the viscosity-dependent parameter, Casson fluid parameter, and expansion ratio. The fluid velocity near the lower wall increases with the Casson fluid parameter but decreases after the mid-point. The fluid velocity is more affected by the temperature-dependent viscosity parameter for Newtonian fluid than non-Newtonian fluid. The results showed that as the Prandtl number increases, the temperature decreases, while the temperature increases with an increase in the Radiation parameter. Also, An increase in the wall expansion ratio leads to higher wall temperatures, whereas a decrease in the power-law index results in reduced temperatures. The results we've acquired were cross-referenced with prior studies, revealing that the employed methods exhibit high precision. The novelty of the present work is obtaining new results through the use of Akbari-Ganji's semi-analytical method.

The effects of thermal radiation, thermal conductivity, and variable viscosity on ferrofluid in porous medium under magnetic field

Purpose This study aims to analyze the two-dimensional ferrofluid flow in porous media. The effects of changes in parameters such as permeability parameter, buoyancy parameter, Reynolds and Prandtl numbers, radiation parameter, velocity slip parameter, energy dissipation parameter and viscosity parameter on the velocity and temperature profile are displayed numerically and graphically. Design/methodology/approach By using simplification, nonlinear differential equations are converted into ordinary nonlinear equations. Modeling is done in the Cartesian coordinate system. The finite element method (FEM) and the Akbari-Ganji method (AGM) are used to solve the present problem. The finite element model determines each parameter’s effect on the fluid’s velocity and temperature. Findings The results show that if the viscosity parameter increases, the temperature of the fluid increases, but the velocity of the fluid decreases. As can be seen in the figures, by increasing the permeability parameter, a reduction in velocity and an enhancement in fluid temperature are observed. When the Reynolds number increases, an increase in fluid velocity and temperature is observed. If the speed slip parameter increases, the speed decreases, and as the energy dissipation parameter increases, the temperature also increases. Originality/value When considering factors like thermal conductivity and variable viscosity in this context, they can significantly impact velocity slippage conditions. The primary objective of the present study is to assess the influence of thermal conductivity parameters and variable viscosity within a porous medium on ferrofluid behavior. This particular flow configuration is chosen due to the essential role of ferrofluids and their extensive use in engineering, industry and medicine.

Mathematical modeling of non-linear reaction-diffusion process in autocatalytic reaction: Akbari-Ganji method

A theoretical model of the electroreduction of halogen oxoanions via autocatalytic redox mediation by halide anions is discussed. This autocatalytic process depends upon a system reaction-diffusion equation including a nonlinear term for homogeneous reactions. This study solves these equations using the robust and user-friendly analytical technique, the Akbari-Ganji method. The current and the redox component concentration are presented in terms of the rate constant. The influence of variables on current is examined using sensitivity analysis. The most important factor affecting current is the ratio between the bulk concentrations of halogen molecules and non-electroactive halogen oxoanions. The theoretically predicted results are compared with the numerical results. These approximate results enhance our understanding of system behavior.

Thermal analysis of nanofluid magnetic flow on a rotating disk in the presence of radiation considering response surface method

This study examines Titania nanofluids that conduct electricity and are combined with various base fluids, focusing on various aspects. A magnetic field analyzes a continuous flow of nanofluid over a rotating disk that is positioned at an angle with a three-dimensional geometry assumption. The continuity, momentum, and energy balance equations are established, transformed using similarity variables, and solved through Akbari–Ganji Method (AGM) and Homotopy Perturbation Method (HPM) semi-analytical methods. The effects of several parameters, such as Magnetic parameter (M), Hall parameter (m), Porosity parameter ([Formula: see text]), Radiation parameter (Rd), and Thickness of liquid ([Formula: see text]), are examined through a graphical representation of state variables, including skin friction and Nusselt number. Additionally, the Response Surface Method (RSM) method has been utilized to simultaneously display the effects of porosity parameters and various factors across the disk. The findings showed that the magnetic, porosity, Hall, and thickness parameters had a significant impact on the behavior of the nanofluid. Specifically, the magnetic field had a strong influence on the velocity and temperature distribution of the fluid as it flowed over the rotating disk, while changes in porosity, Hall, and thickness parameters also affected these state variables.

A novel technique to analyze the fractional model of Williamson and Casson non-Newtonian boundary layer flow

PurposeThe current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.Design/methodology/approachThe trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.FindingsThe profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.Originality/valueMoreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.

Analytical and numerical investigation of heat transfer of porous fin in a local thermal non-equilibrium state

This research employs a local thermal non-equilibrium (LTNE) model to analyze the heat transfer phenomenon through a porous fin, considering natural convection and radiation effects. The infiltration velocity within the porous medium is evaluated using the Darcy model, and buoyancy effects are accounted for using the Boussinesq approximation. The Akbari-Ganji method (AGM) is applied to address the governing energy equations. The accuracy of the proposed solution is verified by comparing it with numerical results obtained from the finite difference method (FDM), the finite element method (FEM), and earlier investigations. The results are presented regarding the total average Nusselt number and temperature profiles. These results shed light on the influence of several important parameters, such as the thermal conductivity ratio, dimensionless thickness, convectional heat transfer, and external and internal radiation. The analysis reveals that decreasing Rayleigh and Biot numbers reduces the temperature profiles of the solid phase. Additionally, when the Rayleigh number is low but the assigned Biot number is high, the temperature difference between the solid and fluid phases diminishes. Furthermore, increased thermal conductivity ratio and dimensionless thickness for assigned Biot and Rayleigh numbers lead to higher solid phase temperatures. The Nusselt number exhibits a decreasing trend with a decreasing thermal conductivity ratio but increases with higher Rayleigh and Biot numbers and increased external radiation.

Analysis of amperometric biosensor utilizing synergistic substrates conversion: Akbari-Ganji's method

Analysis of amperometric biosensor utilizing synergistic substrates conversion: Akbari-Ganji's method

Mathematical analysis of urea amperometric biosensor with Non-Competitive inhibition for Non-Linear Reaction-Diffusion equations with Michaelis-Menten kinetics

This article examines a mathematical model for stable urea amperometric biosensors with non-competitive inhibition under homogenous conditions. The system is based on reaction and diffusion equations with a non-linear component associated with the Michaelis-Menten kinetics of the enzyme reaction. Theoretical findings in this study can be used to examine the impact of various factors, including the Michaelis-Menten constant and the Thiele modulus. The steady-state non-linear reaction–diffusion equations were solved using two effective and widely used analytical approaches, the Akbari-Ganji method (AGM) and the differential transform method (DTM). The generalized approximation analytical solution for the concentrations of the substrate, inhibitor, and product, as well as the current for the experimental values of the parameter, is developed. The current can also be used to analyze the resistance and sensitivity of biosensors. The digital simulation was carried out utilizing MATLAB software. The numerical results help to validate the analytical results. The impact of membrane thickness, maximum enzymatic rate, and substrate concentration on biosensor response was evaluated.

Modeling the effect of processing parameters on temperature history in Directed Energy Deposition: an analytical and finite element approach

PurposeThe purpose of this paper is to assess the feasibility of analytical models, specifically the radial basis function method, Akbari–Ganji method and Gaussian method, in conjunction with the finite element method. The aim is to examine the impact of processing parameters on temperature history.Design/methodology/approachThrough analytical investigation and finite element simulation, this research examines the influence of processing parameters on temperature history. Simufact software with a thermomechanical approach was used for finite element simulation, while radial basis function, Akbari–Ganji and Gaussian methods were used for analytical modeling to solve the heat transfer differential equation.FindingsThe accuracy of both finite element and analytical methods was validated with about 90%. The findings revealed direct relationships between thermal conductivity (from 100 to 200), laser power (from 400 to 800 W), heat source depth (from 0.35 to 0.75) and power absorption coefficient (from 0.4 to 0.8). Increasing the values of these parameters led to higher temperature history. On the other hand, density (from 7,600 to 8,200), emission coefficient (from 0.5 to 0.7) and convective heat transfer (from 35 to 90) exhibited an inverse relationship with temperature history.Originality/valueThe application of analytical modeling, particularly the utilization of the Akbari–Ganji, radial basis functions and Gaussian methods, showcases an innovative approach to studying directed energy deposition. This analytical investigation offers an alternative to relying solely on experimental procedures, potentially saving time and resources in the optimization of DED processes.