Analytic Solution of Spine Cylindrical Porous Fin with Temperature Heat Transfer Coefficient and Emissivity via CM and HPM

摘要

In the present study, the problem of nonlinear equations arising in Spine Cylindrical Porous Fin with Temperature Dependent Heat transfer Coefficient and Emissivity is investigated. The Maxwell equations have been used, and also Rosseland approximation for radiation heat transfer and Darcy model for simulating the flow in porous medium have been adapted. The governing equations are reduced to a nonlinear ODE. The fin is supposed to be an insulated tip fin, which is exposed to a magnetic field. The Collocation Method (CM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the CM in comparison with Homotopy Perturbation Method and numerical method namely Boundary Value Problem method (BVP) in solving this problems. The results reveal that CM is very effective and simple and can be applied for other nonlinear problems.