ABSTRACT Two-dimensional modeling and numerical analysis of a straight fin with convection-radiation heat transfer are presented. The energy equation is adopted to model a fin with rectangular profile in a flow field with streamwise-variable convective heat transfer coefficient. A finite difference technique is used to discertize this equation and a numerical solution is obtained via an iterative scheme. Temperature profiles of the fin surface, fin efficiency and the heat dissipated per unit mass of the fin material are predicted at different flow velocities and thermal conditions. Also, an attempt is proposed to reduce the weight of the straight fin and in accordance to minimize the pumping power by providing a nonuniform fin-height profile. This optimum profile is estimated by tracing the local effective fine heights that maximize the heat dissipated per unit mass. New correlations based on the present predictions are obtained for the fin effective height, fin efficiency and heat dissipated per unit mass as functions of the flow velocity, fin geometry, fin material-properties and the operating base temperature.