Applicable conditions for the simplified calculation of heat transfer for straight fins of uniform cross-section

With the help of a theoretical analysis method a fin-end adiabatic calculation formula is often used instead of a formula based on a fin-end convection heat exchange to calculate the heat transfer of straight fins of uniform cross-section. The approximate error thus obtained can be expressed as a function of the ratio of cross-sectional area to lateral area f/(Uh) and also as a function of Biot number Bi. Through a calculation of the possible range of selected values it has been found that when one of the following two conditions is met, the error of the above calculation method will be less than 1%. The two conditions are 1. The ratio of f/(Uh) of the straight fins is less than 0.5; 2. Number of Bi is greater than 7.