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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.

Akbari-Ganjis method AGM to chemical reactor design for non-isothermal and non-adiabatic of mixed flow reactors