Decomposition Solution for Nonlinear Model Describing Diffusional Growth of Intermetallic Layers

H. Fatoorehchia, R. Rachb aSchool of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran bThe George Adomian Center for Applied Mathematics, 316 South Maple Str., Hartford, MI 49057-1225, USA

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We investigate the solution of a system of two nonlinear ordinary differential equations that are aimed to represent the diffusional growth of intermetallic layers. Firstly, we formulate an equivalent second-order ordinary differential equation for the general system. Afterwards, to treat the model analytically, we apply a powerful, yet simple method known as the Adomian decomposition method to calculate the convergent sequence of analytic functions which approximate the exact solution of the original problem as closely as we desire. For the sake of illustration, a real-world example is presented modeling the growth dynamics of Al3Mg2 and Al12Mg17. An excellent agreement is obtained between the experimental data and the model estimates.

DOI:10.12693/APhysPolA.140.91 topics: intermetallics, diffusion, kinetics, Adomian decomposition