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

,

with and .

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 .

The Demonstration plots the contours of the dimensionless temperature for a user-set value of the Biot number. This solution is based on Chebyshev orthogonal collocation with collocation points.

The analytical solution of the differential equation obtained by separation of variables [1] is given by:

, where is the Biot number and are the zeros of the nonlinear function: .

We have found excellent agreement between our numerical solution and the analytical solution.