Boubaker Polynomials Expansion Scheme Research Articles

Steam gasification of wood biomass in a fluidized biocatalytic system bed gasifier: A model development and validation using experiment and Boubaker Polynomials Expansion Scheme BPES

One of the most important issues in biomass biocatalytic gasification is the correct prediction of gasification products, with particular attention to the Topping Atmosphere Residues (TARs). In this work, performedwithin the European 7FP UNIfHY project, we develops and validate experimentally a model which is able of predicting the outputs,including TARs, of a steam-fluidized bed biomass gasifier. Pine wood was chosen as biomass feedstock: the products obtained in pyrolysis tests are the relevant model input. Hydrodynamics and chemical properties of the reacting system are considered: the hydrodynamic approach is based on the two phase theory of fluidization, meanwhile the chemical model is based on the kinetic equations for the heterogeneous and homogenous reactions. The derived differentials equations for the gasifier at steady state were implemented MATLAB. Solution was consecutively carried out using the Boubaker Polynomials Expansion Scheme by varying steam/biomass ratio (0.5-1) and operating temperature (750-850°C).The comparison between models and experimental results showed that the model is able of predicting gas mole fractions and production rate including most of the representative TARs compounds

Soluciones aproximadas de la dinámica de infección de VIH-1 con tasa de curación

En este trabajo, se presentan dos soluciones aproximadas del modelo de la dinámica de infección de VIH-1 con tasa de curación. Las soluciones propuestas se obtienen usando el método de perturbación homotópica, por sus siglas en inglés (HPM) y el esquema de expansión polinomial de Boubaker por sus siglas en inglés (BPES). Al comparar las soluciones obtenidas vemos que HPM y BPES son herramientas muy potentes para resolver modelos no lineales de infecciones virales.

Analytical approximation for Landau’s constants by using the Boubaker Polynomials Expansion Scheme method

In this study, approximation formulas for evaluating Landau constants are elaborated by using the Boubaker Polynomials Expansion Scheme (BPES). Results are compared to some referred studies.

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

Radiative radial fin with temperature-dependent thermal conductivity is analyzed. The calculations are carried out by using differential transformation method (DTM), which is a seminumerical-analytical solution technique that can be applied to various types of differential equations, as well as the Boubaker polynomials expansion scheme (BPES). By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced and then applied to the aforementioned equations. Solutions are subsequently obtained by a process of inverse transformation. The current results are then compared with previously obtained results using variational iteration method (VIM), Adomian decomposition method (ADM), homotopy analysis method (HAM), and numerical solution (NS) in order to verify the accuracy of the proposed method. The findings reveal that both BPES and DTM can achieve suitable results in predicting the solution of such problems. After these verifications, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as radiation-conduction fin parameter, radiation sink temperature, heat generation, and thermal conductivity parameters.

Enhanced Homotopy Perturbation Method (EHPM) and Boubaker Polynomials Expansion Scheme (BPES) Comparative Solutions to Partial Differential Equations Systems Governing Non-isothermal Tubular Chemical Reactors

In this paper, the Enhanced Homotopy Perturbation Method (EHPM) has been applied along with the Boubaker polynomials Expansion Scheme (BPES) to a system of nonlinear partial differential equations which governs non-isothermal tubular chemical reactors. Theoretical considerations have been discussed in order to illustrate the reliability of the methods. Comparison of EHPM results with those of BPES showed that both techniques are effective and convenient.

Approximation for Transient of Nonlinear Circuits Using RHPM and BPES Methods

The microelectronics area constantly demands better and improved circuit simulation tools. Therefore, in this paper, rational homotopy perturbation method and Boubaker Polynomials Expansion Scheme are applied to a differential equation from a nonlinear circuit. Comparing the results obtained by both techniques revealed that they are effective and convenient.

Accurate solution for motion of a spherical solid particle in plane Couette Newtonian fluid mechanical flow using HPM–Padé approximant and the Boubaker polynomials expansion scheme BPES

In this paper the analytical solutions for the motion of a spherical particle in a plane Couette Newtonian fluid flow are investigated, by using homotopy perturbation method (HPM) and Padé approximant and the Boubaker polynomials expansion scheme (BPES). The current results are then compared with those derived from HPM and the established fourth order Runge–Kutta method in order to verify the accuracy of the proposed method. It is found that this method can achieve more suitable results compare with HPM.

Study of the Phan-Thien–Tanner Equation of Viscoelastic Blood Non- Newtonian Flow in a Pipe-Shaped Artery under an Emotion-Induced Pressure Gradient

In this paper, a three-dimensional, unsteady state non-Newtonian fluid flow in a pipe-shaped artery of viscoelastic blood is considered in the presence of emotion-induced pressure gradient. The results have been expressed in terms of radial profiles of both axial velocity and viscosity and were presented numerically by using the shooting technique coupled with the Newtonian method and the Boubaker polynomials expansion scheme. The effects of some parameters on the dynamics are analyzed.

A Confirmed Model to Polymer Core-Shell Structured Nanofibers Deposited via Coaxial Electrospinning

A model to core-shell structured polymer nanofibers deposited via coaxial electrospinning is presented. Investigations are based on a modified Jacobi-Gauss collocation spectral method, proposed along with the Boubaker Polynomials Expansion Scheme (BPES), for providing solution to a nonlinear Lane-Emden-type equation. The spatial approximation has been based on shifted Jacobi polynomials with was n the polynomial degree. The Boubaker Polynomials Expansion Scheme (BPES) main features, concerning the embedded boundary conditions, have been outlined. The modified Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the technique, and a comparison is made with existing results. It has been revealed that both methods are easy to implement and yield very accurate results.

A Boubaker Polynomials Expansion Scheme for Solving the Flow of Nonlinear Power-Law Fluid in Semi-Solid State

The problem of an uncompressible power-law fluid has long been the challenge in semi-solid forming area. In this paper, the flow of a power-law fluid film on an unsteady stretching surface is analyzed by the means of Boubaker Polynomials Expansion Scheme (BPES). Analytic solutions were given and compared with the numerical results for some real power-law index and the unsteadiness parameter in wide ranges. The good agreement between them showed BPES could be used effectively to solve the flow of nonlinear power-law fluid in semi-solid state.

Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis

The Boubaker polynomials are investigated in this paper. Using a Riordan matrices analysis, a sequence of relations outlining the relations with Chebyshev and Fermat polynomials has been obtained. The obtained expressions are a meaningful supplement to recent applied physics studies using the Boubaker polynomials expansion scheme (BPES).

An attempt to solve neutron transport equation inside supercritical water nuclear reactors using the Boubaker Polynomials Expansion Scheme

In this paper, we use a polynomial scheme for solving the system of nonlinear boundary value problems associated with nuclear fission inside supercritical water nuclear reactors. The results are calculated in terms of series with easily computable components. The suggested method is applied without any discretization or transformation, but under some restrictive assumptions. To illustrate the implementation and efficiency of the proposed method, plots of the wavelength-dependent neutron flux profile are provided. Key words: Supercritical water nuclear reactors (SCWNR), neutron transport equation, distribution function, Boubaker Polynomial Expansion Scheme (BPES), neutron angular flux.

Boubaker Polynomials Expansion Scheme Solution to the Heat Transfer Equation Inside Laser Heated Biological Tissues

In this study, an analytical solution to the heat transfer equation in biological tissues during laser heating is presented. The results were compared to recently published numerical simulations.

Investigations of accretion disk evidence and features in weak-line/classical T Tauri stars using BPES and EVIM

In this paper, a gas sphere model of weak-line classical T Tauri stars is investigated based on the Enhanced Variational Iteration Method (EVIM) and the Boubaker Polynomials Expansion Scheme (BPES). Solutions for the implemented second-order differential equations are obtained and quantitatively analyzed. The analytical results reveal many interesting features of the main patterns of accretion disks found in some relevant published studies.

Physical Investigation of on Nuclear Dynamics Equations in Nanoenergy Reactors Using a High D-O-F Variable Separation Protocol along with the Boubaker Polynomials Expansion Scheme BPES

We present general analytical solutions to the nuclear dynamics-related Neutron Boltzmann Transport Equation inside nanoenergy reactors. Finding a particular solution to the neutron equation by making use of boundary conditions and initial conditions may be too much for the present study and reduce the generality of the solutions. Some simple assumptions have been introduced in the main system thanks to the Boubaker Polynomial Expansion Scheme, BPES, in order to make the general analytical procedure simple and adaptable for solving similar real-life problems.

Effects of Viscous Dissipation on the Thermal Boundary Layer of Pseudoplastic Power-Law Non-Newtonian Fluids Using Discretization Method and the Boubaker Polynomials Expansion Scheme

Heat transfer of pseudoplastic power-law non-Newtonian fluids aligned with a semi-infinite plate is studied. Unlike in most classical works, the effects of viscous dissipation which is coupled with the temperature-dependent thermal diffusivity are considered in the energy equation. The discretization method is used to convert the governing partial differential equations into a set of nonlinear ordinary differential equations. The solutions are presented numerically by using the shooting technique coupled with the Newtonian method and the Boubaker polynomials expansion scheme. The effects of power-law index and the Zheng number on the dynamics are analyzed. The associated heat-transfer characteristics are also tabulated in some domains of the said parameters.

Application of the BPES to Lane–Emden equations governing polytropic and isothermal gas spheres

We apply the Boubaker Polynomials Expansion Scheme (BPES) in order to obtain analytical–numerical solutions to two separate Lane–Emden problems: the Lane–Emden initial value problem of the first kind (describing the gravitational potential of a self-gravitating spherically symmetric polytropic gas), the Lane–Emden initial value problem of the second kind (describing isothermal gas spheres embedded in a pressurized medium at the maximum possible mass allowing for hydrostatic equilibrium). Both types of problems are simultaneously singular and nonlinear, and hence can be challenging to solve either numerically or analytically. We find that the BPES allows us to compute numerical solutions to both types of problems, and an error analysis demonstrates the accuracy of the method. In all cases, we demonstrate that relative error can be controlled to less than 1%. Furthermore, we compare our results to those of Hunter (2001). [Hunter, C., 2001. Series solutions for polytropes and the isothermal sphere. Monthly Notices of the Royal Astronomical Society, 328 839–847] and Mirza (2009). Approximate analytical solutions of the Lane–Emden equation for a self-gravitating isothermal gas sphere. Monthly Notices of the Royal Astronomical Society, 395 2288–2291. in order to demonstrate the accuracy of our method.

Comparative Analysis of Free Optical Vibration of Lamination Composite Optical Beams Using the Boubaker Polynomials Expansion Scheme and the Differential Quadrature Method

The effects of stacking sequences of composite laminated optical beams on free vibration frequencies are investigated using two methods: the Boubaker Polynomials Expansion Scheme (pbes) and the Differential Quadrature Method (dqm). In the last decades, these two techniques have been separately performed for obtaining accurate numerical solutions to several initial boundary value problems (Vo et al. 2010, Li et al. 2008, Chen 2003, Hu et al. 2008, Karami et al. 2003, Malekzadeh et al. 2004, Khare et al. 2004, Della and Shu 2005, Ramtekkar et al. 2002, Adam 2003). Conjointly yielded results are compared and discussed.

Polytropic star structure analysis under Bonnor–Ebert gas sphere astrophysical configuration thorough investigating analytical solutions to the related Lane–Emden equation

In this paper, Bonnor–Ebert gas sphere model of polytropic stars has been investigated through an analytical approach. Two confirmed and well-established methods have been used: the Enhanced Lagrangian Formulation Method ELFM and the Boubaker Polynomials Expansion Scheme BPES. Solutions to the related generalized Lane–Emden equation of the second kind have been expressed and plotted. Results have given evidence to the relevance of the dimensionless Bonnor–Ebert radius, in good agreement with some recently proposed profiles.

Jacobi Pseudo-Spectral Method JPSM and BPES for Solving Differential Equations

In this paper, a shifted Jacobi pseudo-spectral method JPSM is proposed, along with the Boubaker Polynomials Expansion Scheme BPES, for solving a nonlinear Lane–Emden type equation. The Boubaker Polynomials Expansion Scheme BPES main feature, concerning the embedded boundary conditions, have been outlined. The shifted Jacobi-Gauss points are used as collocation nodes. A numerical example has been included to demonstrate the validity and applicability of the two techniques. It has been revealed that both methods are easy to implement and yield very accurate results.