It has long been recognized that the use of fins can facilitate an augmentation of the heat exchange between two fluids which are separated by a solid interface, e.g. in home ‘radiators’, cooling systems in cars and refrigerators, etc. The fins offer a convenient and practical means of achieving a large heat transfer surface without the use of excessive amounts of primary surface.

In this project a simple one-dimensional model will be developed for the heat flow in an isolated fin of arbitrary shape. The resulting governing first-order ordinary differential equation will be solved analytically in some simple cases. This will require some knowledge of Bessel functions. Also some numerical solutions will be sought in more complex situations, e.g. when radiation effects are taken into account.

Extension of the above theories may include some of the following:

  1. Optimisation of the shape of the fin to maximize the heat transfer for a given amount of metal.
  2. The effects of the walls onto which the fins are attached.
  3. The effects of ice or dust being formed on the fins.