Fin (extended surface)

In the study of heat transfer, fins are surfaces that extend from an object to increase the rate of heat transfer to or from the environment by increasing convection. The amount of conduction, convection, or radiation of an object determines the amount of heat it transfers. Increasing the temperature gradient between the object and the environment, increasing the convection heat transfer coefficient, or increasing the surface area of the object increases the heat transfer. Sometimes it is not feasible or economical to change the first two options. Thus, adding a fin to an object, increases the surface area and can sometimes be an economical solution to heat transfer problems.

To create a tractable equation for the heat transfer of a fin, many assumptions need to be made:

With these assumptions, conservation of energy can be used to create an energy balance for a differential cross section of the fin:

Fourier’s law states that

where ${\displaystyle A_{c}}$ is the cross-sectional area of the differential element. Furthermore, the convective heat flux can be determined via the definition of the heat transfer coefficient h,

where ${\displaystyle T_{\infty }}$ is the temperature of the surroundings. The differential convective heat flux can then be determined from the perimeter of the fin cross-section P,

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