An Analytic Solution to a Parameterized Problems Arising in Heat Transfer Equations by Optimal Homotopy Analysis Method

Hany Nasr HASSAN; Mourad Samir SEMARY

Authors

Hany Nasr HASSAN Department of Basic Science, Faculty of Engineering, Benha University, Benha 13512
Mourad Samir SEMARY Department of Basic Science, Faculty of Engineering, Benha University, Benha 13512

Keywords:

Optimal homotopy analysis method, Series solutions, Heat transfer, Fin efficiency, The square residual error, Two-boundary value problem, Convergence-controller parameter

Abstract

In this paper, an accurate approximate solutions for 2 problems arising in heat transfer straight fins are presented using optimal homotopy analysis method (OHAM). The approximated solutions are obtained at different values of parameters for the 2 problems are illustrated, and the fin efficiency is also evaluated. Moreover, the 2 problems are of nonlinear convective-radiative conduction and power-law fin-type. The obtained series solutions of OHAM are compared with the numerical solution (using Mathematica solver) and exact solutions. The square residual error is obtained to verify the accuracy of the presented method.

doi:10.14456/WJST.2014.87

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