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A constant heat transfer coefficient is often assumed in the computation of the temperature distribution along an extended surface. This assumption permits the use of well-established closed form analytical solution thus simplifying the mathematical complexity of the conservation energy equation. For certain fin geometries, this assumption will lead to poor prediction of the thermal performance of the extended surface especially for tapered and triangular fins. In this study, a generalized analytical solution that permits the computation of heat loss from extended surface based on variable heat transfer coefficient, fin geometry and surface curvature was developed. A parametric study of the influence of these parameters on fin efficiency was performed for various boundary layer conditions.