In this paper, analytical solutions for dimensionless fin temperature distribution and dimensionless fin heat transfer rate are derived and offered for a two-dimensional orthotropic, pin fin structure with contact resistance at the fin base in a convective environment. Fin performance was evaluated based on the different forms of ratio of conductive resistance to convective resistance parameters Bi_r, Bi_z, Bi_c, thermal conductivity ratio K^∗, and dimensionless length of fin contact space at the base δ^∗. The detailed discussions on dimensionless parameters lead to the deterministic design and optimization of polymer composite fin structures under all types of convective situations in many real-time applications.