A concave parabolic fin with variable fin base thickness is optimized using a two-dimensional analytical method. In this optimization procedure, heat convection from inside fluid to inside wall, heat conduction from inside wall to fin base and heat conduction through fin base are considered simultaneously as the fin base boundary condition. The maximum heat loss and corresponding fin length and fin base height for fixed fin volumes are referred to as optimum heat loss, optimum fin length, and optimum fin base height, respectively.  These optimum values are presented as a function of inside fluid convection characteristic number, fin base thickness, fin volume, and ambient convection characteristic number. One of the results shows that both optimum heat loss and optimum fin length decreases linearly as fin base thickness increases.

concave parabolic fin, convection characteristic numbers, fin base thickness, fin length, fin volume, heat loss.