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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.

Series Solution for Steady Heat Transfer in a Heat-Generating Fin with Convection and Radiation