With the advent ofhigh speed digital computers, it now appears feasible to reconsider the problem of optimizing a given heat transfer surface with respect to the space variables. In this paper this has been done for a fin tube heat transfer surface. Work to be published later shows that this same procedure can be extended to other types of surfaces. Also, in this paper enough of the detail about the derivation of the equations is included so that anyone interested in adapting this procedure to his problem can easily do so. It should be noted that the earlier work of Schmidt is utilized.