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
). 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),
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