Cooling with a Shaped Pin Fin

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.
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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