Abstract In this article, the problem of a parabolic profiled fin dissipating heat by natural convection to quiescent non-Newtonian fluid has been solved theoretically. The generalized equations of temperature distribution and heat transfer rates have been generated using the appropriate boundary conditions with different flow behavior index (n). The results obtained from the graphs indicated that there is a significant influence of flow behavior index (n) and fin parameter (M) on the local and average heat transfer coefficient. The results further indicated that for a wide range of fin parameters, the local heat transfer coefficients are exhibiting non-monotonically varying characteristics along the length of fin. Keywords: Non-Newtonian fluid, Nusselt number, Prandtl numberCite this Article Ravi Kumar Sangewar. Performance Evaluation of an Arbitrary Profiled Vertical Fin in Non-Newtonian Medium. Journal of Thermal Engineering and Applications. 2016; 3(3): 20–26p.