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Fin (extended surface) : ウィキペディア英語版
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.
== General case ==

To create a tractable equation for the heat transfer of a fin, many assumptions need to be made:
# 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, conservation of energy can be used to create an energy balance for a differential cross section of the fin:
:\dot(x+dx)=\dot(x)+d\dot_.
Fourier’s law states that
:\dot(x)=-kA_c \left ( \frac \right ),
where 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,
:q''=h\left (T-T_\infty\right ),
where 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,
:d\dot_=Ph\left (T-T_\infty\right )dx.
The equation of energy conservation can now be expressed in terms of temperature,
:-kA_c \left.\left ( \frac \right )\right\vert_ = -kA_c \left.\left ( \frac \right )\right\vert_ + Ph\left (T-T_\infty\right )dx.
Rearranging this equation and using the definition of the derivative yields the following differential equation for temperature,
:k\frac\left(A_c\frac\right) + Ph\left (T-T_\infty\right) = 0;
the derivative on the left can be expanded to the most general form of the fin equation,
:kA_c\frac + k\frac\frac + Ph\left (T-T_\infty\right) = 0.
Note that the cross-sectional area, perimeter, and temperature can all be functions of x.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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