Fin (Extended Surface)

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In the study of heat transfer, a **fin** is a surface that extends 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 difference 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 economical or it is not feasible to change the first two options. Adding a fin to an object, however, increases the surface area and can sometimes be an economical solution to heat transfer problems.

## Simplified Case

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

Assume:

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

<math>q_x=q_+dq_,</math>

Fourierâ€™s law states that

<math>q_x=-kA_c left ( frac right )</math>,

where <math>A_c</math> is the cross-sectional area of the differential element. Therefore the conduction rate at x+dx can be expressed...

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Assume:

- Steady state
- Constant material properties (independent of temperature)
- No internal heat generation
- One-dimensional conduction
- Uniform cross-sectional area
- Uniform convection across the surface area

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

<math>q_x=q_+dq_,</math>

Fourierâ€™s law states that

<math>q_x=-kA_c left ( frac right )</math>,

where <math>A_c</math> is the cross-sectional area of the differential element. Therefore the conduction rate at x+dx can be expressed...

Read More

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