Abstract
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.
Highlights
In this study, a mixed flow reactor is investigated through resolving a set of nonlinear differential equations governing its chemical reactions by a new analytical method
The interaction of chemical reactions in chemical reactors attracted the attention of many researchers according to the complexity of the reaction kinetics since the knowledge of real performance of reactions in reactors is helpful in the analysis and design process of reactors and are of great importance for researchers in the fields of mechanical and chemical engineering
A complicated set of nonlinear differential equations have been introduced and analyzed completely by (AGM) and the obtained results have been compared with the numerical method (Runge-Kutta) to show the ability of Akbari-Ganji's Method (AGM) for solving such problems
Summary
A mixed flow reactor is investigated through resolving a set of nonlinear differential equations governing its chemical reactions by a new analytical method. Sci. method capable of solving nonlinear differential equations governing the design of chemical reactors has been presented entitled AGM (Akbari-Ganji’s method) which can be applied in all of the fields of engineering and basic sciences because of its high precision and convergence in dealing with problems with high nonlinearity. Equation 3 and in order to make a set of equations consisting of (n+1) equations and (n+1) the unknown, we confronted a number of additional unknowns which are the coefficients of Equation 3 To resolve this problem, we should derive m times from Equation 1 according to the additional unknowns in the aforementioned set of differential equations and this is the time to apply the boundary conditions of Equation 2 as follows. The dimensionless form of Equations 13 and 14 can be written as follow:
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