We consider the heat transfer problems associated with
a periodic array of triangular, longitudinal, axisymmetric
and pin fins. The problems are modeled as a wall where
the flat side is isothermal and the other side, which
has extended surfaces/fins, is
subjected to convection with
a uniform heat transfer coefficient.
Hence our analysis differs from the classical
approach because (i) we consider multi-dimensional heat conduction
and (ii) the wall, that the fins are attached, is included in the analysis.
The latter results in a non-isothermal temperature distribution
along the base of the fin.
The Biot number (Bi=h~t/k) characterizing the heat transfer
process is defined with respect to the
thickness/radius of the fins (t).
Numerical results demonstrate that the fins would enhance the heat
transfer rate only if the Biot number is less
than a critical value which, in general depends on the geometrical
parameters, i.e. the thickness of the wall, the length of the fins
and the period. For pin fins, similar to rectangular fins, the
critical Biot is independent of the geometry and is approximately
equal to 3.1. The physical argument is that, under strong convection,
a thick fin introduces an additional resistance to heat conduction.