Akbari MR1*, Sara Akbari2 and Esmaeil Kalantari2
1Department of Chemical Engineering and Civil Engineering, Iran
2Department of Chemical Engineering, Iran
*Corresponding author: Akbari MR, Department of Chemical Engineering and Civil Engineering, Iran
Submission: February 24, 2020;Published: March 17, 2020
ISSN: 2832-4439 Volume2 Issue1
In this paper, our aims are accuracy, capabilities and power at solving set of the complex non-linear differential at the reaction chemical. 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-Sara’s Method” or “ASM”.
In this literature, we have set nonlinear differential equations governing of kinetic the plug reactor to chemical reaction [1,2], that can be investigated and resolved response and the actual reactions at reactors for scientists and engineers is very important, because they know the real answer for analysis and design of reactors against chemical reactions are important and highly sensitive in of executive tasks are created. Other methods compared to ASM do not have this ability to gain the solution of the presented problem in high precision and accuracy so nonlinear differential equations such as the presented problem in this case study should be solved by utilizing new approaches like AGM, Akbari Ganji Method [3-8]; (Figure 1). We consider a well-mixed continuous stirred tank reactor with the reaction and set of nonlinear differential equations. parameters F(the flow rate), CA0 (the initial molar concentration) , TA0 (the initial temperature),Q (the rate of heat input to the reactor), V(the volume of the reactor), E, ΔH, k0 (the pre-exponential constant reaction), cp and ρ denote the heat capacity and density of the fluid in the reactor.
Figure 1: A comparison between ASM and Numerical solution for concentration and temperature.
Set of nonlinear differential equations as follows:>
The solution of the mentioned problem by ASM will be obtained as follows:
The following new variables are introduced as:
By selecting the physical values at below:
The solution is rewritten as follows:
ASM and AGM (Akbari-Sara’s Method and Akbari-Ganji Methods) have been invented mainly by Mohammadreza Akbari (MR kbari) in 2019 and 2014 respectively in order to provide a good service for researchers who are a pioneer in the field of nonlinear differential equations. It is worthy to note that I am really grateful to all those who encouraged me to devise these methods which are highly beneficial for analytical solving coupled nonlinear ODEs (especially ASM) in Engineering, basic Sciences and Economic.
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