Nonlinear thermal analysis of serrated fins by using homotopy perturbation method

Thermal analysis of serrated fins which are consist of annular and plain sections are investigated. Serrated fin's thermal conductivity is assumed to change linearly with temperature. Nonlinear differential equations are obtained by applying the energy balance equation for both sections of the serrated fin and these equations are solved by applying homotopy perturbation method. Insulated fin tip, constant fin base temperature and common boundary conditions between the interface of two sections are considered. Serrated fin radii ratio (epsilon), segment height ratio (delta), thermo-geometric fin parameter (psi) and thermal conductivity parameter (beta) effecting the thermal performance and temperature distribution are investigated. The results showed that the homotopy perturbation is a reliable method for the solutions of such nonlinear differential equations. A very good agreement with the homotopy perturbation method and the numerical finite difference method are obtained. It is seen that, serrated fin efficiency lays between annular and rectangular fins and increases with the increase of segment height ratio and thermal conductivity parameter. Such as, fin efficiency values under the condition of epsilon = 2, psi(1) = 1.0 and beta = 0 for delta = 0, 0.5, and 1 are 0.692, 0.718, and 0.762, respectively.