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Application of He’s variational iteration method to nonlinear heat transfer equations. (English) Zbl 1217.80067
Summary: Instead of finding a small parameter for solving nonlinear problems through perturbation method, a new analytical method called He’s variational iteration method (VIM) is introduced to be applied to solve nonlinear heat transfer equations in this Letter. In this research, variational iteration method is used to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative-conduction equation containing two small parameters of ${ϵ}_{1}$ and ${ϵ}_{2}$ and evaluate the efficiency of straight fins. VIM can apply to the nonlinear equations with boundary or initial conditions defined in different points just with developing the correction functional using the extra parameters such as ${C}_{n}$, as used in this Letter.
##### MSC:
 80A20 Heat and mass transfer, heat flow 49S05 Variational principles of physics 35K61 Nonlinear parabolic equations, nonlinear initial boundary value problems