Cooling with a Shaped Pin Fin

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In electronic systems, a fin is a heat sink (passive heat exchanger) that cools a device by dissipating heat to the surrounding medium (e.g. air). Such a pin fin is used to maximize heat transfer to a fluid between two walls.

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A pin fin has an elliptical external surface, as shown in the "pin fin image".

The walls are at a high temperature . The fluid flowing over the pin has a free stream temperature . The coefficient of heat transfer between the pin wall and the surrounding medium is labeled (in ). If one introduces the dimensionless temperature

, the governing equation is:

.

The associated boundary conditions are then:

(axial symmetry condition),

(radial symmetry condition),

(continuity of heat flux at the boundary fin/surrounding air), and

(constant temperature at the wall),

where is the thermal conductivity of the cylindrical pin fin and .

This Demonstration plots the contours of the dimensionless temperature for a user-set value of the Biot number and the shape factor .

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Contributed by: Housam Binous, Ahmed Bellagi, and Brian G. Higgins (September 2015)
Open content licensed under CC BY-NC-SA


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