Series solution for steady heat transfer in a heat-generating fin with convection and radiation

Abstract

The steady heat transfer in a heat-generating fin with simultaneous surface convection and radiation is studied analytically using optimal homotopy asymptotic method (OHAM). The steady response of the fin depends on the convection-conduction parameter, radiation-conduction parameter, heat generation parameter, and dimensionless sink temperature. The heat transfer problem is modeled using two-point boundary value conditions. The results of the dimensionless temperature profile for different values of convection-conduction, radiation-conduction, heat generation, and sink temperature parameters are presented graphically and in tabular form. Comparison of the solution using OHAM with homotopy analysis method (HAM) and Runge-Kutta-Fehlberg fourth-fifth-order numerical method for various values of controlling parameters is presented. The comparison shows that the OHAM results are in excellent agreement with NM. © 2013 Fazle Mabood et al.