Cooling with a Shaped Pin Fin

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 .


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



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.