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An approximation of the analytic solution of some nonlinear heat transfer in fin and 3D diffusion equations using HAM
Author(s) -
Bararnia H.,
Domairry G.,
Gorji M.,
Rezania A.
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20404
Subject(s) - homotopy analysis method , mathematics , nonlinear system , partial differential equation , fin , homotopy perturbation method , heat transfer , heat equation , mathematical analysis , convergence (economics) , series (stratigraphy) , convergent series , homotopy , thermodynamics , power series , physics , biology , paleontology , materials science , quantum mechanics , pure mathematics , economics , composite material , economic growth
In this article, the approximate solution of nonlinear heat diffusion and heat transfer equation are developed via homotopy analysis method (HAM). This method is a strong and easy‐to‐use analytic tool for investigating nonlinear problems, which does not need small parameters. HAM contains the auxiliary parameter ħ, which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter ħ, we can obtain reasonable solutions for large modulus. In this study, we compare HAM results, with those of homotopy perturbation method and the exact solutions. The first differential equation to be solved is a straight fin with a temperature‐dependent thermal conductivity and the second one is the two‐ and three‐dimensional unsteady diffusion problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010