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.
Thus, adding a fin to an object, increases the surface area and can sometimes be an economical solution to heat transfer problems.
One-piece finned heat sinks are produced by extrusion, casting, skiving, or milling.
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:[1] Fourier’s law states that where
The differential convective heat flux can then be determined from the perimeter of the fin cross-section P, The equation of energy conservation can now be expressed in terms of temperature, Rearranging this equation and using the definition of the derivative yields the following differential equation for temperature, the derivative on the left can be expanded to the most general form of the fin equation, The cross-sectional area, perimeter, and temperature can all be functions of x.
The base of the fin is typically set to a constant reference temperature,
) conditions, however: the tip can be exposed to convective heat transfer, insulated, held at a constant temperature, or so far away from the base as to reach the ambient temperature.
For the first case, the second boundary condition is that there is free convection at the tip.
Therefore, which simplifies to The two boundary conditions can now be combined to produce This equation can be solved for the constants
A similar approach can be used to find the constants of integration for the remaining cases.
For the second case, the tip is assumed to be insulated, or in other words to have a heat flux of zero.
Therefore, the boundary condition is: For the fourth and final case, the fin is assumed to be infinitely long.
Therefore, the boundary condition is: Finally, we can use the temperature distribution and Fourier's law at the base of the fin to determine the overall rate of heat transfer, The results of the solution process are summarized in the table below.
) to the heat transfer rate of the object if it had no fin.
is the sum of the heat transfer from the unfinned base area and all of the fins.
Open cavities are defined as the regions formed between adjacent fins and stand for the essential promoters of nucleate boiling or condensation.
From 2004 until now, many researchers have been motivated to search for the optimal design of cavities.
[2] Fins are most commonly used in heat exchanging devices such as radiators in cars, computer CPU heatsinks, and heat exchangers in power plants.
[5] Nature has also taken advantage of the phenomena of fins; the ears of jackrabbits and fennec foxes act as fins to release heat from the blood that flows through them.
