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) andRunge-Kutta-Fehlberg fourth-fifth-ordernumerical method for various values of controlling parameters is presented. The comparison shows that the OHAM results are in excellent agreement with NM.