It is noticed that the buoyantly convective flow of non-Newtonian fluids equipped in the closed cavities is not investigated at the large frame in comparison with the viscous fluids. This is because of the complication of computational boundaries. Therefore, the present analysis is a notable attempt to examine the non-Newtonian fluid equipped in a rhombus-shaped enclosure. The heated T-shaped fin is embedded in a flow field to report the heat transfer aspects. The no-slip condition is implemented at boundary walls of the enclosure and T-shaped fin. The rhombus cavity rooted with T-shaped fin comprises of the cold, adiabatic and heated boundary assumptions. The physical problem is controlled in terms of the differential system. For solution purpose, the finite element method is utilized. It is noticed that the stream function maximized and minimized in an equal magnitude towards Rayleigh number. It is observed that the average Nusselt number along the T-shaped fin is found an increasing function of Rayleigh number. The Casson fluid temperature along the vertical line of fin shows inciting nature for both the Casson fluid parameter and Rayleigh number.