The purpose of this paper is to find a new way of fin design to minimize the irreversibilities due to heat transfer and fluid friction and maximize the available work of the working fluid. The general entropy generation formulas for fins are derived at first according to the first and second law of thermodynamics

then a theoretical analysis on cylindrical pin fins and rectangular straight fins is made by using the above formulas. The minimum entropy generation formulas for these two types of fins are obtained and a principle for fin optimization is proposed

where the minimum entropy generation is chosen to be the objective function to be studied. The effect of different parameters on fin entropy generation is discussed in detail in forced convection heat transfer.