Two-dimensional performance of convecting-radiating fins of different profile shapes

A finite element approach is used to investigate the two-dimensional performance of convecting-radiating fins of rectangular, trapezoidal, triangular, and concave parabolic shapes. The heat transfer rate depends on fin size parameter α, Biot numberBi, radiation-conduction parameterN _r , and environment temperatures θ_∞ and θ _r . Numerical results for the heat transfer rate and the error due to one-dimensional assumption are presented and discussed for each geometry. The highest heat dissipation is achieved with the concave parabolic shape and the lowest with the rectangular shape with the trapezoidal and triangular shapes falling in between. The maximum error of +144 percent is noted for a short and thick rectangular fin (α=1) and ?47 percent for a long thin triangular fin (α=20).