Akbari-Ganji's Method Research Articles

A theoretical investigation of steady-state concentration processes at a carrier-mediated transport model using Akbari-Ganji and differential transform methods

In this article, a carrier-mediated transport model is considered. The steady-state non-linear diffusion equations were solved by two effective and accessible analytical methods, Akbari-Ganji and the differential transform methods. Here, we present the generalized approximate analytical solution for the substrate, product, and reactant concentrations for the small experimental values of the kinetic and diffusion parameters. The numerical solution to this problem was derived using the Mat-lab/Scilab program, showing a satisfactory agreement between the analytical and numerical/computational outcomes. The simulated results can be compared to the relevant theories. This result through the physical parameters shows that the Akbari-Ganji method is better than the differential transform method. The effects of this study are applicable across the entire solution domain. Furthermore, the concentration of species, facilitation factor F, and the reaction equilibrium constant K are compared to the parameters are also obtained.

Nano/micro-beam deflections: Investigation of subjected forces and applications

Micro- and Nano beam MEMS devices possess a broad range of applications owing to their capability to produce precise mechanical motion and sensing capabilities at a small scale. In the field of biomedicine, these devices have been employed in applications such as tissue engineering, lab-on-a-chip systems, and implantable devices. Medical devices, particularly those involved in drug delivery, are significantly impacted by the forces applied to them. Therefore, it is imperative to carefully evaluate the effects of axial force and optimize the device's design to ensure that it can endure the forces it will encounter during operation. Despite being relatively weak, the van der Waals force warrants careful consideration when working at the micro- and nanoscales. In this research, the nonlinear equation obtained by the Galerkin method for a doubly clamped nano/micro-beam under the effect of Van der Waals (vdW) force was solved. The Homotopy Perturbation Method (HPM) and the Akbari Ganji Method (AGM) are introduced to investigate the nonlinear problem in this paper analytically. To validate and investigate the accuracy of the AG and HP methods, the obtained results were compared to the Runge-Kutta approach. The obtained results for all data sets showed the high accuracy of the AG and HP methods. Also, this paper investigated the effect of axial force N on beam type N/MEMS deflection. The axial force N effect in both tensional (N > 0) and compressive (N < 0) modes has been investigated. Due to the obtained results, increasing the axial force compressively increases the deflection of the beam. However, this trend is reversed for the tensional axial force.

Analytical expression for the model that describes the heterogeneous reaction-diffusion process with immobilized enzyme (penicillin G acylase)

This research article examines the reaction-diffusion process in an immobilized enzyme batch reactor. The model incorporates strongly non-linear factors that are associated with standard Michaelis-Menten kinetics. The non-linear reaction-diffusion equations for substrate and product concentrations have been approximated analytically. Employing two different semi-analytical methods, Akbari-Ganji's method (AGM) and the modified Adomian decomposition method (MADM), to compute the dimensionless steady-state solutions to the system of non-linear differential equations for all values of reaction parameters. In addition, the dynamics of the mean integrated effectiveness factor of penicillin acylase in porous spherical particles have been presented for the determination of the local effectiveness factor. In order to gauge the potency of our proposed solution, we compare two semi-analytical results with a numerical result that are in good agreement across the whole concentration range. The proposed formulation aims to simulate the dynamic performance of the system utilizing the parameters and would enhance the determination of the optimum particle size for enzyme catalysts.

Analysis of temperature-dependent thermal conductivity and fin efficiency: Direct Akbari-Ganji method

The vast majority of engineering issues, particularly heat transport equations, have a non-linear form. The analytical solution of temperature distribution, fin effectiveness, and fin efficiency of straight convective fins that transport heat with temperature-dependent thermal conductivity convection is derived in this work using the Direct Akbari-Ganji method (DAGM). DAGM is an effective methodology that is very simple and takes less time to solve non-linear temperature distribution fin problems. In the present investigation, Direct Akbari-Ganji technique offers desirable solutions to heat transfer problems. The round-off error is smaller compared to other methods. For the purpose of calibrating the error accuracy of the suggested direct technique, this result is compared with the numerical and earlier solution. The outcomes show that the DAGM for heat transfer equations in engineering situations has excellent validity and considerable promise. Finally, it is clear that when the thermo-geometric fin parameter increases, so does the fin efficiency. The homogeneity of the fin is due to the variable thermal conductivity. Four convection conditions with constant coefficients, growing and decaying convection coefficient with fin temperature are discussed.

Using analytical methods for finding the approximate solutions to fractional differential equations

This essay focuses on studying the nonlinear fractional integral equation. Various methods, including Akbari-Ganji's Method (AGM), Homotopy Perturbation Method (HPM), and Vibrational Iteration Method (VIM), are utilized to obtain its solution. We introduce an innovative approach to obtain rough approximations for fractional differential equations. These equations play a significant role in the field of fluid dynamics and find widespread application. In this article, we have used analytical methods to check the correctness of the answers. Maple mathematical software is used to solve all fractional equations. Ordinary equations and fractional differential equations have connections to entropy, wavelets, and other related concepts. To demonstrate the method, a few examples are employed, chosen for their accuracy and simplicity of implementation. The solutions are explained using convergent series. According to the calculations performed with analytical methods on the fractional integral equations of the nonlinear oscillator, Due to the swing movements of the oscillator, as the swing movement's increase, the velocity gradient becomes an upward trend.

Theory for Electrochemical Heat Sources and Exothermic Explosions: The Akbari–Ganji Method

A device that transforms chemical energy into electrical energy is an electrochemical cell. The reaction type inside the cell determines whether it is exothermic or endothermic. This paper discusses the mathematical modelling of exothermic explosions in a slab. This model is based on a nonlinear equation containing a nonlinear term related to Arrhenius, bimolecular, and sensitised laws of reaction kinetics. The absolute temperature can be derived by solving the nonlinear equation using the Akbari–Ganji technique. The mathematical model also numerically solved and simulated in the MATLAB® v2016b software. The new simple theoretical result is validated with previously identified analytical and numerical findings. The influence of the parameters of Frank-Kamenetskii number, activation energy and the numerical exponent on temperature is discussed. The Frank-Kamenetskii number is observed to drop as the temperature is found to decrease, while the activation energy parameter is shown to increase. The numerical exponent has little or no effect on the temperature. An extension of this model to cylinder and sphere geometry is also provided.

Analytical analyzing mixed convection flow of nanofluid in a vertical channel using python approach

This study uses analytical methods to investigate the impact of parameters on the mixed convection flow of nanofluid in a vertical channel. The research aims to explore the heat transfer characteristics of nanofluids for more efficient heat transfer in devices. The study analyzes the influence of the Reynolds, Grashof, and Prandtl numbers on nanofluid flows. It also examines the effects of temperature and nanoparticle concentration distributions on parameters such as Brownian motion (Nb), thermophoresis (Nt), and Lewis number (Le). The presence of nanoparticles significantly enhances the heat transfer characteristics in the flow problem. Reynolds number, Grashof number, and Prandtl number significantly impact flow behavior. Velocity, temperature, and nanoparticle volume fraction profile trends are thoroughly investigated and found to vary. Akbari-Ganji's method (AGM) and the homotopy perturbation method (HPM) demonstrate the potential of computational tools in analyzing nanotechnology fluid dynamics. The accuracy and reliability of the proposed analytical techniques are confirmed through comparisons with a numerical method. The novelty of this research lies in its comprehensive analysis of parameter effects on the mixed convection flow of nanofluid, the enhanced heat transfer characteristics in the presence of nanoparticles, and the unique contributions offered by the utilization of Python programming in this field. The outcomes of this study provide insights for designing and optimizing heat transfer systems using nanofluids, contributing to advancements in nanotechnology.

A novel technique for solving unsteady three-dimensional brownian motion of a thin film nanofluid flow over a rotating surface.

The motion of the fluid due to the swirling of a disk/sheet has many applications in engineering and industry. Investigating these types of problems is very difficult due to the non-linearity of the governing equations, especially when the governing equations are to be solved analytically. Time is also considered a challenge in problems, and times dependent problems are rare. This study aims to investigate the problem related to a transient rotating angled plate through two analytical techniques for the three-dimensional thin film nanomaterials flow. The geometry of research is a swirling sheet with a three-dimensional unsteady nanomaterial thin-film moment. The problem's governing equations of the conservation of mass, momentum, energy, and concentration are partial differential equations (PDEs). Solving PDEs, especially their analytical solution, is considered a serious challenge, but by using similar variables, they can be converted into ordinary differential equations (ODEs). The derived ODEs are still nonlinear, but it is possible to approximate them analytically with semi-analytical methods. This study transformed the governing PDEs into a set of nonlinear ODEs using appropriate similarity variables. The dimensionless parameters such as Prandtl number, Schmidt number, Brownian motion parameter, thermophoretic parameter, Nusselt, and Sherwood numbers are presented in ODEs, and the impact of these dimensionless parameters was considered in four cases. Every case that is considered in this problem was demonstrated with graphs. This study used modified AGM (Akbari-Ganji Method) and HAN (Hybrid analytical and numerical) methods to solve the ODEs, which are the novelty of the current study. The modified AGM is novel and has made the former AGM more complete. The second semi-analytical technique is the HAN method, and because it has been solved numerically in previous articles, this method has also been used. The new results were obtained using the modified AGM and HAN solutions. The validity of these two analytical solutions was proved when compared with the Runge-Kutta fourth-order (RK4) numerical solutions.

Thermal analysis of Non-Newtonian visco-inelastic fluid MHD flow between rotating disks

Analytical techniques are used in this article to examine the forced flow and heat transfer in a non-Newtonian Reiner-Rivlin fluid between two infinitely revolving disks in a magnetic field. The partial differential equations (PDEs) emphasizing flow and heat transfer were transformed into a nonlinear ordinary differential equations (ODEs) system using the Von Karman similarity transformation. The system of nonlinear ODEs with boundary conditions was solved using the Homotopy Perturbation Method (HPM) and Akbari-Ganji's Method (AGM). The study assessed the effects of physical factors on temperature profiles and the radial, transverse, and axial velocity components, including the visco-inelastic parameter, Reynolds number, Prandtl number, forced parameter, and magnetic field. The Python programming language was used for symbolic and numeric calculations of velocity components and temperature profiles. The accuracy of the results obtained through the analytical approach validates the applicability and efficiency of the proposed approach for studying the forced flow and heat transfer in non-Newtonian fluids between rotating disks.

Theoretical analysis and steady-state responses of the multienzyme amperometric biosensor system for nonlinear reaction-diffusion equations

In this study, a mathematical model for a multienzyme biosensor system is presented. This system identifies analytes by chemical conversion into the signal response. It is based on nonlinear reaction-diffusion equations for a bisubstrate amperometric system under steady-state conditions. A precise parametric analysis is crucial for a better understanding of the nonlinear multienzyme biosensor. The Akbari-Ganji method is used to solve the system of nonlinear differential equations. AGM is already utilized to solve differential equations in heat transfer science. In this study, it is employed for the first time to approximate the solution of a nonlinear multienzyme biosensor. An approximate analytical expression for the concentration of substrate, inhibitor, co-substrate, product 1, product 3 and current are obtained. Furthermore, the current is used to determine the sensitivity and resistance of a biosensor. This study uses the MATLAB tool to describe the numerical simulation of the problem. A satisfactory level of agreement was found between the analytical and simulation results for the experimental parameter values. The influence of the parameters on sensitivity, resistance and current are also investigated using sensitivity analysis. Current and sensitivity are strongly influenced by the substrate concentration in the bulk solution and the glucose reaction constant, respectively. The most significant factor influencing biosensor resistance is membrane thickness. This work serves as a resource for further research into concentration models and sheds light on relevant applications, such as food safety, biomedicine, and environmental research.

Thermal analysis of boundary layer nanofluid flow over the movable plate with internal heat generation, radiation, and viscous dissipation

This study examines the convective flow of a constant, laminar, and incompressible viscous fluid over a plate that moves by the assumption of nanoparticles, such as Al and Cu. In the governing equations, we considered three major effects of heat transfers: radiation, internal heat generation, and viscous dissipation factor. Either we used “similarity transformations” we converted momentum and temperature PDE “Partial Differential Equations” to nonlinear ODE “Ordinary Differential Equations.” Those governing equations were resolved by a new and effective semi-analytic approach named the Akbari-Ganji method (AGM). Comparison of the problem-solving outcomes by the methods used with the outcomes of the previous search exhibits good agreement. When the suction parameter values are increased velocity of the nanofluid is augmented, but temperature reduces with a rising of the suction parameter in both nanofluids. Increasing the λ “slip term of velocity “cause rising values of the velocity term compared with the temperature gradient, which decreases strongly. Also, the temperature and velocity variations are between −0.5 and 1.5.

Reaction kinetics of amperometric enzyme electrode in various geometries using the Akbari-Ganji method

A kinetic model of amperometric enzyme electrodes of planar, cylindrical and spherical shape factors is discussed. This paper considers the mathematical formulation of the kinetics mechanism in the electrode’s diffusion layer. This model comprises a non-linear system of reaction diffusion equations. Simple and closed-form analytical expressions for the dimensionless concentration of mediator, enzyme, substrate and resultant current are gained using the Akbari-Ganji method. Comparing the analytical and numerical results reveals a satisfactory level of agreement. The influence of the parameter and electrode’s geometry on mediator concentration, enzyme concentration and current are analysed.

Mathematical modelling of a mono-enzyme dual amperometric biosensor for enzyme-catalyzed reactions using homotopy analysis and Akbari-Ganji methods

The mathematical model is described in this article as a mono-enzyme dual biosensor. This model involves coupling the enzyme-catalyzed reactions under steady-state conditions for a reaction-diffusion equation describing the substrate and product. Pseudo-experimental responses to chemical mixtures were produced using a computer model of a biocatalytic amperometric biosensor that used a mono-enzyme-catalyzed (nonspecific) competitive conversion of two substrates.The non-linear system of reaction-diffusion equations into an approximate analytical expression is solved by employing the Homotopy Analysis Method (HAM) and Akbari-Ganji Method (AGM) are used. These expressions are compared with numerical simulations carried out using MATLAB. Further, the biosensor's resistance, sensitivity, and current density were analytically expressed.

Evaluation of AGM and FEM method for thermal radiation on nanofluid flow between two tubes in nearness of magnetism field

The nanofluid flow through two orbicular cylinders is explored utilizing the overall Koo–Kleinstreuer–Li (KKL) model within the nearness of a magnetic field. The impact of thermal radiation is considered in the energy equation. The novelty of this study is examining convective heat transfer for nanofluid flow between two flat tubes with the Akbari-Ganji method and Finite Element Techniques to examine the heat flux field by implies of 2D forms of temperature and velocity at unprecedented Reynolds numbers. The approaches for solving ODEs are AGM and FEM. Semi-analytical methods are assessed for specific parameters of aspect ratio, Hartmann number, Eckert number, and Reynolds quantity with various values. Adding Ha, Ec, and G causes the temperature gradient to grow, while adding the Reynolds number causes it to decrease. As the Lorentz forces increase, the velocity decreases; nevertheless, as the Reynolds number rises, the velocity decreases. With the reduction of the fluid's dynamic viscosity, the temperature will decrease, which will decrease the thermal trend along the vertical length of the pipes.

Analytical technique for solving strongly nonlinear oscillator differential equations

The main motivation of this paper is to apply general formulas of the gamma function to find the analytical solutions of some types of nonlinear differential equations with recognizable simplicity and less calculation compared to other existing analytical methods in the literature. The simplicity and accuracy of the Gamma function method (GFM) in solving strongly nonlinear differential equations can be displayed through three practical examples arising in many different fields of engineering and science. The results obtained analytically are compared with the well-known analytical methods already published in the literature, such as Akbari-Ganji's method (AGM), homotopy perturbation method (HPM), and exact numerical solutions to confirm the efficiency of GFM. Excellent agreement is found between the analytical solutions and the exact numerical ones. Accordingly, the GFM is more reliable for exploring approximate solutions for strongly nonlinear oscillators. Moreover, the GFM can be easily extended to other nonlinear problems and is, therefore, very applicable in engineering and applied sciences.

Thermal evaluation of MHD Jeffrey fluid flow in the presence of a heat source and chemical reaction

In this paper, the flow of an incompressible fluid is thermally studied. Investigations into the heat transfer process have been conducted in non-Newtonian fluid flows with chemical reactions and heat sources present. The application of this work is the fluid flow around the stretching sheet; fluid flow on a stretching sheet can be applied to polymer extrusion, drawing or plastic films, hot rolling, casting and other engineering problems. The novelty of this paper is that the governing equations have been solved by a new and efficient semi-analytical approach, the Akbari–Ganji method (AGM). In order to investigate the issue, the finite element method (FEM) has also been applied. Comparing the results of problem-solving with the applied methods with the results of the previous research shows a perfect agreement. The results show that the parameters of Hartmann number and interaction improve the velocity profiles. Additionally, for greater Hartmann number values, raising the parameter of interaction decreases the temperature value, but a smaller value has the reverse effect. As the Hartmann number increases, the fluid velocity decreases and it shows that with the increase of electromagnetic force, the velocity of fluid flow decreases.

The magnetohydrodynamic flow of viscous fluid and heat transfer examination between permeable disks by AGM and FEM

This paper studied a two-dimensional steady, laminar, and incompressible viscous fluid between two porous disks in outer magnetic amplitude. The invention in this essay is broken down into two interconnected parts. In the first part, the dimensionless equations of the nanofluid flow passing between two disks are investigated using the Akbari-Ganji Method (AGM). The findings are compared with those obtained using the numerical method. In the second section, the Finite Element Method (FEM) in CFD software was used to analyze the fluid pressure, velocity, and temperature parameters of two MWCNT and SWCNT nanotubes. Sliding at the limits shifts the turning point toward the upper disc. It is observed that the magnitude of the axial velocity reduces as the Reynolds number increases at any point in the space between the discs. Two critical areas within the fluid locale where the fluid is persistent despite changes in significant parameters are uncovered by contrasts in radial velocity profiles. The heat transmission rate at the lower penetrable circle consistently diminishes within the nearness of slip as the Reynolds number increments. Also, the inverse is genuine at the upper permeable plate.

Theoretical analysis of putrescine enzymatic biosensor with optical oxygen transducer in sensitive layer using Akbari–Ganji method

This article reports a theoretical analysis of the reaction-transport processes of the Putrescine enzymatic biosensor inside the sensitive layer under steady-state conditions. It consists of two substrates with the same reaction rate and depends on non-linear reaction-diffusion equations. A simple approximate analytical expression for the concentration of substrates (Putrescine and Oxygen) and current are obtained analytically using the Akbari-Ganji and homotopy analysis method. Further, the resistance and sensitivity of a biosensor are also determined using the current. The numerical simulation of the problem is presented in this study using the Matlab program. Comparing analytical results with simulation results for the experimental parameter values has shown satisfactory agreement. Also, the effect of the parameters on current is investigated using sensitivity analysis. The most crucial factor affecting current is the sensing layer's oxygen concentration, followed by the kinetics and transport parameters. However, the reciprocal of the square of the Thiele modulus and the putrescine concentration in the sensing layer has the most negligible impact. Our obtained results are useful in optimizing and designing biosensors.

Analytical and numerical investigation of thermal distribution for hybrid nanofluid through an oblique artery with mild stenosis

In this study, the accuracy of three methods to simulate the thermal diffusivity profile in oblique stenosis artery with hybrid nanofluid and the influence of volume fraction and heat sources in the hybrid nanofluid, including Al2O3 and Cu, is studied. Comparing the analytical methods for reliable answers is important in the new studies. Also, the influence of volume fraction and heat source parameter S in temperature evolution is studied. Akbari–Ganji Method (AGM), Finite Element Method (FEM), and Runge–Kutta method are studied to calculate the stenosis artery's heat profile. The results are compared by reference value, AGM is the more accurate method than FEM and Runge–Kutta methods by less than 7 percent error, and FEM is more accurate than Runge–Kutta by less than 9 percent error. The maximum difference between the three methods happened near the wall of the vessel. 0.02, 0.03, and 0.05 is the volume fraction chosen for studying. Changing the volume fraction of nanoparticles is studied by enhancing the volume fraction of Nanoparticles and presenting the Al2O3, and Cu decreases the max temperature profile and increases the heat source by increasing the maximum heat temperature. Al2O3 has more influence on maximum heat temperature and decreases the temperature profile more.

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.