Fin Effectiveness

Fins are used to enhance heat transfer, and the use of fins on a surface cannot be recommended unless the enhancement in heat transfer justifies the added cost and complexity associated with the fins. In fact, there is no assurance that adding fins on a surface will enhance heat transfer. The performance of the fins is judged on the basis of the enhancement in heat transfer relative to the no-fin case.

Thus, we want to answer: What is the advantage of using a fin? The performance of fins is expressed in terms of the fin effectiveness is defined as:

$$\begin{array}{rl}{ϵ}_{\text{fin}}& =\frac{\text{Heat transfer rate from fin of base area }{A}_b}{\text{Heat transfer rate from surface of area }{A}_b}\\ & =\frac{{\dot{Q}}_{\text{fin}}}{{\dot{Q}}_{\text{no fin}}}\\ & =\frac{{\dot{Q}}_{\text{fin}}}{h{A}_b(T_b-T_{\infty })}\end{array}$$

Hence, $A_b$ is the cross-sectional area of the fin at the base, and ${\dot{Q}}_{\text{no fin}}$ represents the rate of heat transfer from this area if no fins are attached to the surface.

How do we interpret efficiency?

• ${ϵ}_{\text{fin}}=1$ indicates that the addition of fins does not affect heat transfer at all.
• ${ϵ}_{\text{fin}}<1$ indicates that the fin actually acts as insulation, slowing down heat transfer from the surface.
• ${ϵ}_{\text{fin}}>1$ indicates that fins are enhancing heat transfer from the surface, as they should.