A rectangular fin with a fluid in the inside wall is analyzed and optimized using a two-dimensional analytical method. The influence of the fluid convection characteristic number in the inside wall and the fin base thickness on the fin base temperature is listed. For the fixed fin volumes, the maximum heat loss and the corresponding optimum fin effectiveness and dimensions as a function of the fin base thickness, convection characteristic numbers ratio, convection characteristic number over the fin, fluid convection characteristic number in the inside wall, and the fin volume are represented. One of the results shows that both the optimum heat loss and the corresponding fin effectiveness increase as the fin base thickness decreases.