Akbari-Ganji's Method Research Articles

Modeling glucose isomerization in a packed- bed reactor: A complete theoretical and numerical approach

Immobilized enzymes are used in many applications in the food industry presently. Some researchers employ apparent kinetic parameters in immobilized enzyme reactor systems, which only apply to these specific case studies. To increase productivity in a packed bed reactor, it is vital to establish a thorough understanding of all the factors affecting the process, including axial dispersion, convective mass transport, intra-particle diffusive mass transfer, and kinetics. This paper discusses the packed-bed reactor's steady-state model of immobilized glucose isomerase. This model is based on a nonlinear reaction-diffusion equation containing nonlinear terms associated with the enzymatic reaction of Michaelis–Menten kinetics. Akbari-Ganji's method (AGM) and Taylors series with Pade's approximation method are used to calculate the species concentration and normalized current for all possible kinetic parameters and Thiele modulus. The saturated and unsaturated kinetics also have been investigated analytically. A significant agreement between the simulation results and the analytical expression of concentration is observed.

Analyzing the effect of radiation on the unsteady 2D MHD Al2O3-water flow through parallel squeezing sheets by AGM and HPM

In this essay, the impact of magnetism amplitude on two-dimensional squeezing nanoparticle stream betwixt two equidistant sheets is inspected. The novelty of this research the dimensionless values of various fluids, such as Prandtel number and friction coefficient, influence the investigation of the velocity and heat transfer parameters of aluminum oxide nanofluid. Three mathematical techniques—AGM, HPM, and NUM—have been used in these experiments, and the outcomes and graphs have been computed and compared using these techniques. The non-dimensioned differential equations have been solved using three methods: Akbari-Ganji Method, Homotopy Perturbation Method, and Numeric technique. A comparison is then made between the resolutions of the presented strategies with the numeric approach in a separate chart. We arrived at the generalization that as the Prandtl number increases, the temperature and thermal of the nanofluid flow increase and its concentration drops, and as the Nusselt number declines. This was done by examining the results of the numerical model that was used to solve the equations. As S is increased, it is seen that the temperature drops while the concentration rises. The Nusselt number has increased in value following the growth in permeability value. Displacement increases along with the heat transfer coefficient.

Rigid plate submerged in a Newtonian fluid and fractional differential equation problems via Caputo fractional derivative

The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject in Newtonian fluids. In this article, the homotopy perturbation method (HPM), the variational iteration method (VIM), and the Akbari–Ganji method (AGM) were used to solve linear fractional differential equations order in fluid mechanics and fractional optimal control problems in the sense of Caputo. Achieving an exact solution to these equations has been one of the researchers’ goals; according to the research results, the proposed methods provide an exact solution. Comparing the results obtained by the proposed methods with those obtained by the Shehu method reveals that the present methods are very effective and convenient in applied fields. Also, the VIM and AGM methods are more proper than HPM in solving these equations. The solutions obtained by the proposed methods agree with the solutions available in the literature.

Thermal analysis of Williamson fluid flow with Lorentz force on the stretching plate

This study is dedicated to the semi-analytical solution of the problem by managing the inclined Lorentz force and variable viscosity impacts on Williamson nanofluid as visco-inelastic fluids on a stretching plate. Varying viscosity is supposed to change with temperature as a linear function. The fundamental mathematical modeled problem, i.e., the system of PDEs, is transformed nonlinear into odes using appropriate transformations. Computational solutions to the issue are also performed through the efficient semi-analytical method. AGM (Akbari-Ganji method) has been used in solving nonlinear coupling equations. Characteristics of some control parameters such as Hartmann number, inclined angle, and stretching index have been considered. Also, the Sherwood number and Nusselt number are described in tables. The results show that the heat transfer rate decreases by increasing the Pr number. Also, increasing the thermophoresis parameter reduces the temperature. Comparing the results obtained from the AGM and previous research shows that the technique used has high accuracy and efficiency.

The solution of Pennes' bio-heat equation with a convection term and nonlinear specific heat capacity using Adomian decomposition

Pennes' bio-heat equation is the most widely used equation to analyze the heat transfer phenomenon associated with hyperthermia and cryoablation treatments of cancer. In this study, the semi-analytical and numerical solutions of Pennes' equation in a highly nonlinear form derived from renal cell carcinoma tissue's nonlinear specific heat capacity along with a freezing convection term were obtained and analyzed for the first time. Here, the governing equation was reduced to a lumped capacity form for simplification and exerted on a solid spherical renal tumor. In the following, two semi-analytical techniques, the adomian decomposition method (ADM) and the Akbari–Ganji's method (AGM) were evaluated in solving the governing ODE. The comparison revealed full conformity between ADM and AGM, in addition to an excellent agreement between the semi-analytical and the numerical results before the phase transition. The analysis highlighted a deviation between the semi-analytical and numerical results for the limited convergence of power-series-based semi-analytical methods throughout the phase change and beyond. For the investigated case with D_{t} = 0.025,quad {text{Biot}} = 0.075, the convergence occurred while tau in [0,0.7] for both methods. Consequently, both semi-analytical techniques ADM and AGM, are applicable to find the solution of Pennes' bio-heat equation before the phase change, and there is no superiority in favor of one in accuracy. In contrast, numerical methods are reliable during the phase transition and after that. The analysis of the numerical solution showed that with the growth of the tumor, achieving the necrosis of the malignant tissue takes longer, and large tumors' temperature may not decrease to necrosis temperature. The interpretation of the numerical results indicated that cryoablation could be considered an effective thermal treatment for renal tumors with a diameter lower than 2.0 cm.

Investigation of nanofluid flow in a vertical channel considering polynomial boundary conditions by Akbari-Ganji's method

In this research, a vertical channel containing a laminar and fully developed nanofluid flow is investigated. The channel surface's boundary conditions for temperature and volume fraction functions are considered qth-order polynomials. The equations related to this problem have been extracted and then solved by the AGM and validated through the Runge-Kutta numerical method and another similar study. In the study, the effect of parameters, including Grashof number, Brownian motion parameter, etc., on the motion, velocity, temperature, and volume fraction of nanofluids have been analyzed. The results demonstrate that increasing the Gr number by 100% will increase the velocity profile function by 78% and decrease the temperature and fraction profiles by 20.87% and 120.75%. Moreover, rising the Brownian motion parameter in five different sizes (0.1, 0.2, 0.3, 0.4, and 0.5) causes lesser velocity, about 24.3% at first and 4.35% at the last level, and a maximum 52.86% increase for temperature and a 24.32% rise for Ψ occurs when Nb rises from 0.1 to 0.2. For all Nt values, at least 55.44%, 18.69%, for F(η), and Ω(η), and 20.23% rise for Ψ(η) function is observed. Furthermore, enlarging the Nr parameter from 0.25 to 0.1 leads F(η) to rise by 199.7%, fluid dimensionless temperature, and dimensional volume fraction to decrease by 18% and 92.3%. In the end, a greater value of q means a more powerful energy source, amplifying all velocity, temperature, and volume fraction functions. The main novelty of this research is the combined convection qth-order polynomials boundary condition applied to the channel walls. Moreover, The AMG semi-analytical method is used as a novel method to solve the governing equations.

Theoretical analysis of reaction-diffusion process in biocatalyst modified electrodes: Solutions derived via Akbari-Ganji method and Taylor’s series with Ancient Chinese algorithms

Theoretical analysis of reaction-diffusion process in biocatalyst modified electrodes: Solutions derived via Akbari-Ganji method and Taylor’s series with Ancient Chinese algorithms

Mathematical modeling of substrate consumption in a biofilm: Solutions arrived using Akbari-Ganji method

Mathematical modeling of substrate consumption in a biofilm: Solutions arrived using Akbari-Ganji method

Importance of induced magnetic field and exponential heat source on convective flow of Casson fluid in a micro-channel via AGM

The study of the natural convective flow of a fluid in the presence of an induced magnetic field has always been of considerable importance due to its many applications in various areas of science, technology, and industry, such as the operation of magnetohydrodynamic generators. This study addresses an analysis of exponential heat source and induced magnetic field on the second-class convection of Casson fluid in a microchannel. The flow is in a vertical microchannel organized by two vertical plates. The answer to governing equations has been grabbed for temperature field, induced magnetic field, and velocity via Akbari-Ganji's method (AGM). Nusselt number, skin friction coefficient, and current density are approximated. Graphs that describe the conclusion of influential physical variables on velocity, temperature, current density, induced magnetic field, and skin friction coefficient distributions are shown. Comparison of results with numerical method (Runge-Kutta-Fehlberg, RKF-45), homotopy perturbation method (HPM), and AGM confirms the accuracy of answers obtained with AGM.

Hydrothermal analysis on non-Newtonian nanofluid flow of blood through porous vessels

In this paper, the flow of non-Newtonian blood fluid with nanoparticles inside a vessel with a porous wall in presence of a magnetic field have been investigated. This study aimed to investigate various parameters such as magnetic field and porosity on velocity, temperature, and concentration profiles. In this research, three different models (Vogel, Reynolds and Constant) for viscosity have been used as an innovation. The governing equations are solved by Akbari-Ganji's Method (AGM) analytical method and the Finite Element Method (FEM) is used to better represent the phenomena in the vessel. The results show that increasing the Gr number, porosity and negative pressure increase the blood velocity and increasing the magnetic field intensity decrease the blood velocity.

Thermal analysis of moving porous fin wetted by hybrid nanofluid with trapezoidal, concave parabolic and convex cross sections

In this study, the thermal performance of moving porous fin wetted with hybrid nanofluid with different cross-sections in the presence of a magnetic field is investigated. As an innovation, three different cross-sections) trapezoidal, concave parabolic and convex (have been used. The Shape-factor effect of hybrid nanoparticles is also considered in the equations. After extracting the governing equations and converting the PDE equations to ODE by Similarity solution, the equations are solved by Akbari-Ganji's method. The boundary conditions are an insulated tip with a finite length, and thermal functions for heat transfer coefficient and conductivity have been assumed. The impacts of several characteristics on the dimensionless temperature are thoroughly investigated, including Peclet number, thermal conductivity parameter, emissivity parameter, heat transfer coefficient parameter, convective–conductive parameter, and radiative–conductive parameter. The results show that Akbari-Ganji's method has good accuracy in solving heat transfer equations related to moving porous fin. Also, increasing the Peclet number increases the dimensionless temperature, because increasing the Peclet number causes the fin to move faster.

Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods

A mathematical model of reaction-diffusion problem with Michaelis-Menten kinetics in catalyst particles of arbitrary shape is investigated. Analytical expressions of the concentration of substrates are derived as functions of the Thiele modulus, the modified Sherwood number, and the Michaelis constant. A Taylor series approach and the Akbari-Ganji's method are utilized to determine the substrate concentration and the effectiveness factor. The effects of the shape factor on the concentration profiles and the effectiveness factor are discussed. In addition to their simple implementations, the proposed analytical approaches are reliable and highly accurate, as it will be shown when compared with numerical simulations.

Analytical solution of nonlinear differential equations two oscillators mechanism using Akbari–Ganji method

In the last decade, many potent analytical methods have been utilized to find the approximate solution of nonlinear differential equations. Some of these methods are energy balance method (EBM), homotopy perturbation method (HPM), variational iteration method (VIM), amplitude frequency formulation (AFF), and max–min approach (MMA). Besides the methods mentioned above, the Akbari–Ganji method (AGM) is a highly efficient analytical method to solve a wide range of nonlinear equations, including heat transfer, mass transfer, and vibration problems. In this study, it was constructed the approximate analytic solution for movement of two mechanical oscillators by employing the AGM. In the derived analytical method, both oscillator motion equations and the sensitivity analysis of the frequency were included. The AGM was validated through comparison against Runge–Kutta fourth-order numerical method and an excellent agreement was achieved. Based on the results, the highest sensitivity of the oscillation frequency is related to the mass. As [Formula: see text] and [Formula: see text] increase, the slope of the system velocity and acceleration will increase.

Suction and injection effect on magnetohydrodynamic fluid flow within a vertical annulus for electrical wire cooling

In this article, natural convection of MHD fluid flow within a vertical annulus is investigated in existence of radial magnetic field and heat generation or absorption. As an innovation effect of suction and injection has been considered in the velocity and temperature equations. governing equations are solved by Akbari-Ganji's analytical method (AGM) and results are compared with numerical method (Runge-Kutta 4th) and LSM method (least square method) for purpose of showing the accuracy of AGM. Studies were performed for various parameters such as: suction and injection parameter (S), heat generation or absorption (H) and Hartmann number (M) under two boundary conditions isothermal and constant heat flux. Results indicate that with increasing heat generation velocity, temperature and mass flow rate in both boundary conditions are increase while opposite trend are observed for increasing heat absorption. velocity of fluid decreases when Hartmann number increase. Also, it is explained that Nusselt number increases with suction and heat absorption parameters and decreases with injection and heat generation parameters. Phenomenon and parameters studied in this work can give a good insight for cooling electronic equipment such as wire cooling.

Akbari–Ganji Method for Solving Equations of Euler–Bernoulli Beam with Quintic Nonlinearity

In many real word applications, beam has nonlinear transversely vibrations. Solving nonlinear beam systems is complicated because of the high dependency of the system variables and boundary conditions. It is important to have an accurate parametric analysis for understanding the nonlinear vibration characteristics. This paper presents an approximate solution of a nonlinear transversely vibrating beam with odd and even nonlinear terms using the Akbari–Ganji Method (AGM). This method is an effective approach to solve nonlinear differential equations. AGM is already used in the heat transfer science for solving differential equations, and in this research for the first time, it is applied to find the approximate solution of a nonlinear transversely vibrating beam. The advantage of creating new boundary conditions in this method in additional to predefined boundary conditions is checked for the proposed nonlinear case. To illustrate the applicability and accuracy of the AGM, the governing equation of transversely vibrating nonlinear beams is treated with different initial conditions. Since simply supported and clamped-clamped structures can be encountered in many engineering applications, these two boundary conditions are considered. The periodic response curves and the natural frequency are obtained by AGM and contrasted with the energy balance method (EBM) and the numerical solution. The results show that the present method has excellent agreements in contrast with numerical and EBM calculations. In most cases, AGM is applied straightforwardly to obtain the nonlinear frequency– amplitude relationship for dynamic behaviour of vibrating beams. The natural frequencies tested for various values of amplitude are clearly stated the AGM is an applicable method for the proposed nonlinear system. It is demonstrated that this technique saves computational time without compromising the accuracy of the solution. This approach can be easily extended to other nonlinear systems and is therefore widely applicable in engineering and other sciences.

A kinetic model for amperometric immobilized enzymes at planar, cylindrical and spherical electrodes: The Akbari-Ganji method

Diffusion and kinetics of amperometric immobilized enzymes on the planar, cylindrical and spherical electrodes are discussed. This model is described as a set of non-linear reaction-diffusion equations consisting of a non-linear term related to Michaelis-Menten kinetics and enzyme-catalyzed reactions. In this paper, we obtain approximately the general analytical solutions for the non-linear equations that describe diffusion-limited reaction within the film by employing the Akbari-Ganji Method (AGM). The obtained analytical results for the concentration of substrate, mediator and current are compared with the available limiting case results and numerical results and found to be in satisfactory agreement. The dependence of the amperometric response on substrate and mediator concentration, enzyme concentration, electrode potential, film thickness and geometry of the electrode is analyzed.

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

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

Squeezing nanofluid flow between parallel rotating plates analysis by AGM method

In this paper, nanofluid flow analysis between two parallel palates is investigated using the Akbari-Ganji Method (AGM). By comparing it with numerical methods it can be concluded that the AGM has high efficiency and acceptable accuracy for solving nonlinear problems with high order of nonlinearity. The partial differential equations governing the fluid flow were converted to ordinary differential equations by using suitable similarity transformation and then the Akbari-Ganji’s Method (AGM) has been used to solve governing equations. In this paper, the effect of adding nano-particles to water, which is flowing between two parallel rotating plates, has been investigated. The chosen nano-particles are Al2O3 and TiO2. The effects of Eckert and squeeze numbers on flow and heat transfer characteristics are investigated. The results show that with the increase in Eckert number, the temperature increases while the velocity profile does not change. On the other hand, with the increase in squeeze number the velocity and temperature profile decrease. Due to the decrease in thermal boundary layer, Nusselt number increases with the increase in Eckert and squeeze numbers. Skin friction doesn't vary with Eckert number, but increasing squeeze number decreases skin friction.

English

In this paper, the chemical reactor with the energy changing (non-isotherm) and non-monotonic reactions in a mixed flow is investigated and also the sets of complex nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. The set of differential equations are consisted of the mass equilibrium and energy (temperature) changing at concentration governing the reactors. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. Comparisons are made between AGM and numerical method (Runge- Kutta45). The results show that this method is very effective and simple and can be applied for other nonlinear problems. Key words: New method, Akbari-Ganji's method (AGM), nonlinear differential equation, mixed flow, non-monotonic reactions, non-adiabatic, reactor design.

Effect of magnetic and boundary parameters on flow characteristics analysis of micropolar ferrofluid through the shrinking sheet with effective thermal conductivity

Ferrofluids have many applications in mechanical and electrical engineering. In this paper, characteristics of ferrofluid over a shrinking sheet with effective thermal conductivity model are studied by the homotopy perturbation method (HPM) and Akbari-Ganji's method (AGM). Also, the Finite Element Method (FEM) has been applied for numerical solution. The governing equations formulated by the Tiwari-Das model. It is supposed that base fluid and nanoparticles are water and Fe3O4respectively. Effect of related parameters of micro-rotation velocity and dimensionless velocity have taken for suction and injection of mass transfer parameter. Results show that the magnetic and boundary parameters, in contrast to the micro-rotation parameter, have the same impact on velocity. Moreover, a comparison has been made between the results of this study with other researchers shows the impressive accuracy and efficiency of these methods.