This paper offers a thorough investigation into convective heat transfer methods, specifically examining forced convection over a smooth sphere and natural convection over a finned sphere. The main objective is to identify the dominant heat transfer mode, employing the Biot number as a discriminating factor. The study delves into the intricate relationship between fin geometry and heat transfer efficiency during natural convection over a finned sphere, aiming to understand the impact of various fin designs on heat exchange efficiency. In the context of forced convection, the study systematically varies fin height from 5 to 15 mm, evaluating its influence on the Nusselt number and overall heat transfer coefficient. This quantification clarifies the precise effect of fin height on heat transfer. Moreover, the research explores the interplay between Rayleigh and Nusselt numbers, unveiling the nuanced dynamics governing heat transfer. The study's ultimate goal is to provide valuable insights for enhancing heat transfer processes in diverse engineering and thermal management applications, contributing to the development of more effective thermal management techniques.