Abstract: A finite element numerical study has been conducted of two-dimensional heat conduction in a rectangular fin with a variable heat transfer coefficient (h_x) in the flow direction. The results show that the predicted fin efficiency with variable local heat transfer coefficient can be significantly lower than when a uniform h_x value is assumed. The fin efficiency is lower because of the spreading resistance associated with the lateral conduction of heat toward the leading edge. The effect of variable h_x was found to increase as the fin Length-to-Width ratio (L/W) decreased. For laminar boundary layer flow at L/W = 1/10, the fin efficiency with variable h_x was as much as 8.7% lower than with a uniform heat transfer coefficient. For a turbulent flow conditions, the effect of variable h_x was found to be less significant.