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In this article, the problem of nonlinear equations arising in fin problem for nucleate boiling is presented and then three analytical methods called . Homotopy Analysis Method (HAM), Homotopy Perturbation Method(HPM) and Variation Iteration Method(VIM ) are employed to compute an approximation for the solution of nonlinear differential equations governing on the problem. The result of the mentioned method is compared with a type of numerical analysis as Boundary Value Problem method (BVP). The results reveal that Homotopy Analysis Method is very effective and simple than other techniques and can be applied for other nonlinear problems specially in heat transfer equation.

Series exact solution of nonlinear differential equation governing in fin problem for nucleate boiling by HAM and comparison with VIM, HPM and BVP