A Circular Fin Protruding from a Hot Wall


Fins are often used as a medium to increase
heat transfer. Joseph, an engineer, is interested in using a circular
fin with radius r_{o} and length L to cool a hot wall. The wall
temperature at the base of protruding fin is T_{o}. The fin is
cooled by a fluid stream at .
Based on constant thermal conductivity and an infinite heat transfer
coefficient assumption, the twodimensional steadystate temperature
distribution of the fin is,
where , and α_{n}'s
are the positive roots of J_{o}(α_{n})
= 0 for n = 1, 2, 3, ... Joseph would like to find the temperature value at
a particular point on the fin.



 J_{o}(α_{n}), the Bessel
function, is zero when
α_{1} = 2.405, α_{2} = 5.520, α_{3} =
8.654, and
α_{4} = 11.792
 Determine the values of the Bessel functions
J_{o}(α_{n}r/r_{o}) and
J_{1}(α_{n}) based on the power
series expansion with at least five terms (Note: This is the approach only
if tables and graphs of Bessel funtion values are not available).
