Efficiency of fin (ηfin):

The efficiency of a fin is defined as the ratio of the actual heat transfer from the fin to that the heat that would be dissipated if whole surface of the fin is maintained at base temperature.

ηfin=Actual heat transferred by the fin (Qfin)Maximum heat that would be transferred if whole surface of the fin is maintained at the base temeratureQmax)

According to the definition, efficiency of the fin of infinite length is given as below ηfin=h.P.K.Ac(ts-ta)h.As(ts-ta)

ηfin=h.P.K.Ach.As

Effectiveness of fin (εfin):

It is defined as the ratio of the actual heat transfer that takes place from the fin to the heat that would be dissipated from the same surface area without fin.

By above definition ε for infinite length fin is given by εfin=h.P.K.Ac(ts-ta)h.Ac(ts-ta)

εfin=P.Kh.Ac

Factors affecting fin effectiveness

1. P.Kh.Ac should be greater than unity if the rate of heat transfer from the primary surface is to be improved.
2. If the ratio of P and Ac is increased , the effectiveness of fin is improved.
3. Use of fin will be more effective with materials of large thermal conductivities.