![Strangkkp](https://upload.wikimedia.org/wikipedia/commons/5/5c/Strangkkp.jpg)
In the study of
heat transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
, fins are surfaces that extend from an object to increase the rate of heat transfer to or from the environment by increasing
convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the conve ...
. The amount of
conduction,
convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the conve ...
, or
radiation of an object determines the amount of heat it transfers. Increasing the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer.
Thermometers are calibrated in various Conversion of units of temperature, temp ...
gradient between the object and the
environment
Environment most often refers to:
__NOTOC__
* Natural environment, all living and non-living things occurring naturally
* Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...
, 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
An economic system, or economic order, is a system of production, resource allocation and distribution of goods and services within a society or a given geographic area. It includes the combination of the various institutions, agencies, entitie ...
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.
One-piece finned heat sinks are produced by
extrusion
Extrusion is a process used to create objects of a fixed cross-sectional profile by pushing material through a die of the desired cross-section. Its two main advantages over other manufacturing processes are its ability to create very complex ...
,
casting
Casting is a manufacturing process in which a liquid material is usually poured into a mold, which contains a hollow cavity of the desired shape, and then allowed to solidify. The solidified part is also known as a ''casting'', which is ejected ...
,
skiving
Skive or skiving may refer to:
* Skive, Denmark, a place in Denmark
** Skive Municipality
** Skive Airport
** Skive station
** Skive fH, a handball club
** Skive IK, a football club
** Skive RC, a rugby club
* Skiving (leathercraft), the thinning ...
, or
milling.
General case
To create a tractable equation for the heat transfer of a fin, many assumptions need to be made:
#
Steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p' ...
# 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, 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
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
is the temperature of the surroundings. 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.
Uniform cross-sectional area
If the fin has a constant cross-section along its length, the area and perimeter are constant and the differential equation for temperature is greatly simplified to
:
where
and
. The constants
and
can now be found by applying the proper boundary conditions.
Solutions
The base of the fin is typically set to a constant reference temperature,
. There are four commonly possible fin tip (
) 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
and
to find the temperature distribution, which is in the table below.
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,
:
For the third case, the temperature at the tip is held constant. 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.
Performance
Fin performance can be described in three different ways. The first is fin effectiveness. It is the ratio of the fin heat transfer rate (
) to the heat transfer rate of the object if it had no fin. The formula for this is:
:
where
is the fin cross-sectional area at the base. Fin performance can also be characterized by fin efficiency. This is the ratio of the fin heat transfer rate to the heat transfer rate of the fin if the entire fin were at the base temperature,
:
in this equation is equal to the surface area of the fin. The fin efficiency will always be less than one, as assuming the temperature throughout the fin is at the base temperature would increase the heat transfer rate.
The third way fin performance can be described is with overall surface efficiency,
:
where
is the total area and
is the sum of the heat transfer from the unfinned base area and all of the fins. This is the efficiency for an array of fins.
File:Low efficiency fins.png, Aluminium heat sink with low efficiency cooling fins
File:High efficiency fins.png, Aluminium heat sink with high efficiency cooling fins.
Inverted fins (cavities)
Open cavities are defined as the regions formed between adjacent fins and stand for the essential promoters of nucleate boiling or condensation. These cavities are usually utilized to extract heat from a variety of heat generating bodies. From 2004 until now, many researchers have been motivated to search for the optimal design of cavities.
Uses
Fins are most commonly used in heat exchanging devices such as
radiators in cars, computer
CPU heatsink
A heat sink (also commonly spelled heatsink) is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant, where it is dissipated away from the device, th ...
s, and
heat exchanger
A heat exchanger is a system used to transfer heat between a source and a working fluid. Heat exchangers are used in both cooling and heating processes. The fluids may be separated by a solid wall to prevent mixing or they may be in direct conta ...
s in
power plant
A power station, also referred to as a power plant and sometimes generating station or generating plant, is an industrial facility for the electricity generation, generation of electric power. Power stations are generally connected to an el ...
s. They are also used in newer technology such as
hydrogen fuel cell
A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen fuel, hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most bat ...
s.
Nature has also taken advantage of the phenomena of fins. The ears of
jackrabbit
Hares and jackrabbits are mammals belonging to the genus ''Lepus''. They are herbivores, and live solitarily or in pairs. They nest in slight depressions called forms, and their young are able to fend for themselves shortly after birth. The gen ...
s and
fennec fox
The fennec fox (''Vulpes zerda'') is a small crepuscular fox native to the deserts of North Africa, ranging from Western Sahara to the Sinai Peninsula. Its most distinctive feature is its unusually large ears, which serve to dissipate heat and ...
es act as fins to release heat from the blood that flows through them.
References
*
{{Authority control
Heat transfer