A Circular Fin Protruding from a
Fins are often used as a medium to increase
heat transfer. Joseph, an engineer, is interested in using a circular
fin with radius ro and length L to cool a hot wall. The wall
temperature at the base of protruding fin is To. The fin is
cooled by a fluid stream at .
Based on constant thermal conductivity and an infinite heat transfer
coefficient assumption, the two-dimensional steady-state temperature
distribution of the fin is,
where , and αn's
are the positive roots of Jo(αn)
= 0 for n = 1, 2, 3, ... Joseph would like to find the temperature value at
a particular point on the fin.
- Jo(αn), the Bessel
function, is zero when
α1 = 2.405, α2 = 5.520, α3 = 8.654, and
α4 = 11.792
- Determine the values of the Bessel functions
Jo(αnr/ro) and J1(αn) 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).