Iris Publishers-Open access Journal of Archives in Biomedical Engineering & Biotechnology | Chemical Reactors Catalyst bed and Analytical Solution of Complicated Partial Nonlinear Differential Equations by new Approach AKLM

 

Authored by MR Akbari*

Abstract

In this paper, for the first time, we investigate and solve a complicated highly partial nonlinear differential equations of chemical reactions in the cylindrical and spherical coordinates on the catalyst bed for the design of chemical reactors. We challenge and prove the power of this method that it can easily analyze the most difficult nonlinear problems in a completely analytical way, which we named it AKLM (Akbari Kalantari Leila’s Method). Certainly we know that the chemical reaction process on the solid catalysts is very complex, and the governing differential equations governing them are nonlinearity complex. In this paper we present a new analytical solution which can easily analyze all such problems and make a great evolution in the nonlinear industries in the reactors design in chemical engineering. Finally, this scientific approach can create a great phenomenon in the analytical solution of nonlinear problems in engineering sciences, especially in the chemical and mechanical engineering.

Keywords: New method; Akbari-Kalantari-Leila’s Method (AKLM); Reactor Catalytic bed; Partial Nonlinear Differential Equation; Cylindrical, Spherical and Cartesian Coordinates

Introduction

In the study, our aims introduce of accuracy, capabilities and power for solving complex non-linear partial differential in the reaction chemical on the reactor’s catalyst bed. AKLM method can be successfully applied in various engineering fields such as mechanics (solid and fluid), electronics, petroleum industry, designing chemical reactors [1,2], and also in applied sciences (physics), economics and so on. It is worth noting that these two methods are convergent at any form of differential equations, including any number of initial and boundary conditions. During the solution procedure, it is not required to convert or simplify the exponential, trigonometric and logarithmic terms, which enables the user to obtain a highly precise solution. Besides, the methodology behind these techniques are completely understandable, easy to use, and users with common knowledge of mathematics will be capable of solving the most complicated equations at low calculation cost. As all experts know most of engineering actual systems behavior in practical are nonlinear process and analytical scrutiny these nonlinear problems are difficult or sometimes impossible. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled “Akbari- Kalantari-Leila Method” or “AKLM”. He’s Amplitude Frequency Formulation method [3-5] which was first presented by Ji-Huan He gives convergent successive approximations of the exact solution and Homotopy perturbation technique HPM [6]. It is necessary to mention that the above methods do not have this ability to gain the In the study, our aims introduce of accuracy, capabilities and power for solving complex non-linear partial differential in the reaction chemical on the reactor’s catalyst bed. AKLM method can be successfully applied in various engineering fields such as mechanics (solid and fluid), electronics, petroleum industry, designing chemical reactors [1,2], and also in applied sciences (physics), economics and so on. It is worth noting that these two methods are convergent at any form of differential equations, including any number of initial and boundary conditions. During the solution procedure, it is not required to convert or simplify the exponential, trigonometric and logarithmic terms, which enables the user to obtain a highly precise solution. Besides, the methodology behind these techniques are completely understandable, easy to use, and users with common knowledge of mathematics will be capable of solving the most complicated equations at low calculation cost. As all experts know most of engineering actual systems behavior in practical are nonlinear process and analytical scrutiny these nonlinear problems are difficult or sometimes impossible. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled “Akbari- Kalantari-Leila Method” or “AKLM”. He’s Amplitude Frequency Formulation method [3-5] which was first presented by Ji-Huan He gives convergent successive approximations of the exact solution and Homotopy perturbation technique HPM [6]. It is necessary to mention that the above methods do not have this ability to gain the

Mathematical formulation of the Problem

We consider an isothermal reaction and also, we assume governing chemical reaction equation on the solid catalyst bed in the chemical reaction are complicated and according of mathematical equations as follows:

1. By assuming that on the catalyst bed the reaction chemical for component A is as follows:

To read more about this article....Open access Journal of Archives in Biomedical Engineering & Biotechnology

Please follow the URL to access more information about this article

https://irispublishers.com/abeb/fulltext/chemical-reactors-catalyst-bed-and-analytical-solution-of-complicated-partial-nonlinear.ID.000601.php

To know more about our Journals...Iris Publishers

To know about Open Access Publishers